Problems in Arithmetic TO SUPPLEMENT THE CALIFORNIA STATE TEXT FOR THE SEVENTH AND EIGHTH GRADES (REVISED) BY S. P. ROBBINS GIFT OF Problems in Arithmetic TO SUPPLEMENT THE CALIFORNIA STATE TEXT FOR THE SEVENTH AND EIGHTH GRADES (REVISED) BY S. P. ROBBINS Principal Oakdale School CHICO, CALIFORNIA HARR WAGNER PUBLISHING CO. 239 Geary St. SAN FRANCISCO, CALIFORNIA Copyright, 1917, By S. P. BOBBINS ENTERPRISE .^^.PR'NT. CHICQ PREFACE. To make the teaching of arithmetic most effective the teacher must have her pupils work many problems be- sides those of the State Series arithmetic. Only by this constant drill with the arithmetical processes become fixed in the mind 01' the child. Accuracy, rapidity and facility in the application of the processes learned to the problems of every day life are the chief ends of instruction in arithmetic. This book of thirteen hundred problems supplies ade- quate material for supplementary work. From it the teacher can select such problems as fit the needs of her school. Trie use of the book in the hands of the pupils will ca found most satisfactory; it will relieve the teacher from dictating problems or copying them on the board. 37785G PROBLEMS IN ARITHMETIC TO SUPPLEMENT THK CALIFORNIA STATE TEXT. FOR THK SEVENTH AND EIGHTH GRIDES. PERCENTAGE Exercise 1. To Supplement Page 166. Write as decimals: 1. 15% 2. 16V 2 % 3. 22%% 4. 6%% 5. 3%% 6. 12V 8 % :7. 45% 8. 7% 9. 2V 2 % 10. y 2 % 11. 414% 12. 14% 13. %% 14. V 8 % 1.5. -5%% 16. %%, 17. y 5 % 18. '%% , 19. %% 20. %% 21. 25% 22. 125% 23. 30% 24. 230% 25. 26. 118%% 27. 103V 2 % 28. 115%% 29. 625V 2 % 30. 222V 5 % 31. 12% 32. 12.2%e 33. 6.4% 34. .4% 35. 1.6% 36. .6% 37. 24.8% 38. .8% 39. 2.25% 40. .75% 41. .1% 42. .11% 43. -154.7% 44. 10.625% 45 .87*% 46. 8.75% 47. 87.5% 48. 137.5% 49. 13.75% 50. 1.375% (4) Exercise 2. Supplement to Page 166. Write as per cents: 1. .50 26. % 2. .05 27. % 3. .25 28. % 4. .09 29. 2%' 5. .36 30. 7V 5 6. 1.75. 31. .361/2 7. .40 32. 13-20 8. .01 33. 7-25 9. 2.00 34. 3-20 10. .37 % 35. .5625 11. 2.45 36. .00625 12. .675. 37. .045 13. .425. 38. .185 14. 1.4375 39. 4.5 15. .0025 40. 8.5 16. .0003 41. .osy 8 17. .009 42. .22% 18. 1.625 43. 1.16% 19. 1.875 44. 4.50 20. 2.165 45. .62i/ 2 21. .004 46. 1.62% 22. .014 47. 1.08 23. .022 48. 1.005 24. .225 49. .0014 25. % 50. .10% (5) Exercise 3. To Supplement Pages 167-168. 1. 1% of $363 28. 2. 9% of $864 29. 3. 7% of $4.35 30. 4. 23% of $435 31. 5. 46% of $2783 32. 6. 38% of $34.60 33. 7. 67% of $386 34. 8. 8% of $40.50 35 9. 3% of $222 36. 10. 16% of $27.86 37. 11. 5% of 1200 bu. 38. 12. 13% of 3200 Ib. 39. 13. 10% of 4567 yd. 40. 14. 16y 3 % of 336 41. 15. 24% of $47.25 42. 16. 14% of $375 43. 17. 26% of $562 44. 18. 5% of $83.40 45. 19. 7% of $60.86 46. 20. 36% of $37.50 47. 21. 85% of $84.26 48. 22. 6% of $264.50 49. 23. 12% of $4,500 50. 24. 44% of $7,084 51. 25. 75% of $342.34 52. 26. 92% of $620.72 53. 27. 8% of $409.25 54. 55. 1.5% of 2,256 (6) 5 2-7% of $46.55 7V 5 % of $87.50 3V 3 % of $18.75 18%% of $25.60 6V 2 % of $850 . 112% of $1420.75 121% of $2000 145% of 1275 167% of 345.25 132% of 900 4.4%) of 875 7.5% of 1560 5.2% of 37,500 acres. 8*4% of 16,800 1.2% of 1,615.30 .2% of 938 .5% of 1580 .8% of 15,625 15% of 6,400 3.7% of 1,250 .9% of 450 1-W% of 5,000 acres %% of 800 bbl. 10.57* of $204,624.20 14% of 7,000 7% of 50,000 .11% of .10,000 Exercise 4. To Supplement Pages 170-171. Find by using common fractions: 1. 25% of $4,644 2. 40% of $225.25 3. 33V 3 % of $9,930.30 4. 75% of $15,948 5. 16%% of $734.65 6. 66 2-3% of $10,293.60 7. 60% of $600 8. 80% of $6,400 9. 20% of $186,971.50 10. I2y 2 % of $880 11. 6 1 / 49c of $32,000 12. 8V3% of $96,586.25 25. 30% of 13. 10% of $4,753.75 14. 11 1-9% of $24,716.20 15. 62%% of $128 16. 22 2-9% of $7856 17. 14 2-1% of $777.75 18. 44 4-9% of $860 19. 77 7-9% of $490.90 20. 28 4-7% of $2,294 21. 37%% of $873 22. 87%% of $16,820.80 23. 8%% of $976 24. 83%% of $4,412.40 $10,202 Exercise 5. To Supplement Pages 170-171. "Find : 1. 6% of 243 ft. 2. 3%% of 368 yd. 3. 12%% of $336.48 4. 13V 2 % of 984 qt. 5. 66%% of 729 gal. 6. 44% of $841 7. 16%% of $549 8. 87%% of 968 men. 9. 6 1 /4%o of 682 acres. 10. %% of 904 sq. rd. 11. 9% of 785 Ib. 12. 105% of $213.81 13. 110% of $496.28 14. 137%% of $620.80 15. 225% of $391.04 16. 308%% of $845.37 17. 14% of $36,928 18. 120% of $624.50 19. %% of 40,000 books. 20. 12%% of $275.20. 21. 12% of 950 mi. 22. 18% of $1,440 23. 24% of $2,160 24. 35% of $1,750 25. 115% of $3,462 26. 25% of $93.84 27. 33%%; of $46.08 28. 37%% of $91.36 29. 250% of $316.48 30. 16 2-3% of $79.74 31. 175% of $546.84 32. 162%% of $74.24 (7) 33. 166%% of $97.89 42. 5% of $410.50 34. 20% of $2,650.25 43. 6% of $1,175 35. 30% of $970.40 44. 7% of $875 36. 4% of $8,600 45. 8% of $7,935 37. 2.2% of $18,475.60 46. 9% of $80.75 38. 87%% of $688 47. 10% of $19,335.35 39. .01% of $215,540 48. 13% of $878.50 40. 3% of $285.10 49. 7.5% of $1,200 41. 4% of $1,234.50 50. 3.5% of $1,608.80 Exercise 6. To Supplement Pages 172-173. 1. How much is $448.64 plus 25% of itself? 2. How much is $369.36 less 33^% of itself? 3. How much is 125 % of $246.80? 4. How much is 125% of $1,234.40? 5. What is the interest on $750 for 1 year at 6. How much is 93% of $623? Of $275? 7. If a village formerly of 1,460 inhabitants, has gained 5% in population, what is the population now? 8. A real estate agent sold a house and lot for $7,580 and received 5% for his services. How much did he re- ceive? 9. I owed A. R. Smith $1,450. I paid him 40% of it at one time, 20% of the remainder at another time, and 10% of what then remained at another time; how much did I then owe him? 10. A merchant sold silk that cost $1.75 per yard at a loss of 4%. How much was the loss on each yard? What was the selling price? 11. A man bought a watch for $26.25, and sold it at a loss of 8%. Find the selling price. (8) 12. A man bought a horse for $380, and sold it at a gain of 5%. How much did he receive for it? 13. An agent sold a piano that cost $320, gaming 27V 2 %. What was the selling price? 14. A man built two houses at a cost of $3,864 each. He sold one at a gain of 15% and the other at a loss of 3%. What was the net gain? 15. A farmer received $16 a ton for his hay. It passed through the hands of a shipper, a jobber and a retailer, who gained respectively 12y 2 %, 3V 3 % and 20%. What was the retail price? 16. A carriage dealer has two carriages that cost him $178 each. He sold one at a gain of 15% and the other at a loss of 24%. Find the net loss. 17. Mr. Jones sold property that cost him $4,580 at a gain of 12 1 / 2 %. He invested the proceeds of the sale in land at $150 per acre. How many acres of land did he buy? 18. Which is the greater, and how much, 18% of $980.20 or SSVs of $620.20? 19. A man invested $15,550 in land at $225 per acre. Six months later he sold the land at $275 an acre, paying the agent 4% of the price of sale. What was the net gain on the entire transaction? 20. Mr. Stone willed 25% of his property to his son, to his daughter, and the remainder to a library. The estate amounted to $153,600. How much did each lega- tee receive? 21. A merchant having $6,120, invested 12^% of it in dry goods and 16% of the remainder in groceries. How much did he pay for both? 22. What is the difference between 19% of $2,635 and 15% of $3,267? 23. A man invested $4,850 and gained 22% during the year. How much was the capital at closing? (9) Exercise 7. To Supplement Pages 171-178. Find the number of which Find the sum of which 1. 840 is 20% 11. $504 is 28% 2. 420 is 8% 12. $880 is 55% 3. 252 is 18% 13. $24.84 is 6% 4. 720 is 32% 14. $36.95 is 4% 5. 75 is 40% 15. $43.47 is 42% 6. 987 is 47% 16. $93.60 is 64% 7. 45 is 2V2% 17. 68.22 is 75% 8. 225 is 15% 18. $79.62 is 37V 2 % 9. 176 is 20% 19. $87.89 is 17% 10. 384 is 25% 20. $374.10 is 43% 21. 148.2 is 15.6% of what number? 22. 225.4 is 18.4% of what number? 23. 7,375.5 is 39.6% of what number? 24. 11,988 is 55.5% of what number? 25. 154.35 is 12.25% of what number? 26. 780.60 is 62V 2 % of what number? 27. 639.45 is 66%% of what number? 28. 1,364.65 is 83V 3 % of what number? 29. 92.24 is 80% of what number? 30. 2,010.60 is 75% of what number? 31. 63.30 is 33V 3 % of what number? 32. 125.70 is 12%% of what number? 33. 475 is 16%% of what number? 34. 828.50 is 14 2-7% of what number? 35. 250 is 8Vs% of what number? 36. 716.26 is 40% of what number? 37. 50.42 is 90% of what number? 38. 3,291.25 is 200% of what number? 39. 4,500 is 120% of what number? 40. 600 is 133y 3 % of what number? (10) 42. 499.20 is 175% of what number? 43. 625 is 166%% of what number? 44. 546.68 is 150% of what number? 45. 1,100 is 105% of what numebr? 46. 1,596 is 133% of what number? 47. 1,980 is 144% of what number? 48. 1,032 is 107V 2 % of what number? 49. 3,775.8 is 101.5% of what number? 50. 1,260 is 100y 5 % of what number? Exercise 8, To Snplement Pages 174-178. 1. If 14% of a number is 9646, what is the number? 2. If 16%% of a number is 432, what is the number? 6. 1,400 is 16 2-3% more that what number? 4. 1200 is 25% less than what number? 5. A man spent $365, which was 12^% of all the money he had. How much money had he? 6. An agent's commission for buying land was $134.40. If he was allowed 3^%, what was the amount of pur- chase? 7. A man spent $37.50, which was 6%% of all his money. How much had he? 8. Sold a horse at a profit of $15.50, thereby gaining What was the selling price? 9. Sold a watch at a loss of 12%%, thereby losing $5.50. What was the selling price? 10. A pays $17.50 a month for his board, which is 14% of his salary. What is his yearly salary? 11. A sold his farm for $12,818 more than it cost him, gaining 17% of the cost. Find the cost and the sel- ling price. 12. A man received $468.75 from a bankrupt, which was 37^% of the sum due. What was the sum due? (11) 13. What was the amount of a bill upon which a col- lector received $14.76 for collecting at 4%% 14. A farmer sold his farm for $1296 less than it cost him, wjiich was a loss of 18%. Find the cost. 15. A man paid $38.40 for insuring his house at For how much was the policy written? 16. The interest at 6% for one year on a certain sum was $50.40. What was the sum at interest? 17. A man sold his horse at a gain of $37, and this was 16% of the cost. Find the cost. 18. A merchant's assets amount to $6,082.20. This will pay 62% of his debts. How much does he owe? 19. A wholesale grocer sold 375 bbls. of sugar, which was 75% of all he had. How many barrels had he re- maining? 20. A manufacturer owned 60% of a foundry and sold 15% of his share for $4,500. What was the value of the entire foundry. 21. A field produced 1,470 bushels of oats last year and that was 42% of what it produced this year. This year's crop was sold for 45 cents per bushel. Find the amount received. 22. A quantity of rice lost 20% of its weight in being hulled at the mill. If the hulls weighed 4,752 Ib. what was was the weight of the rough rice? 23. In six hours 6,000 tons of coal were loaded on a vessel. If this was 80% of her load, how many tons did she carry? 24. If the shrinkage of a quantity of wheat in drying was 2% and amounted to 775 pounds, how much did the wheat weigh before drying? 25. If 32% of the people in a certain city are voters, and there are 40,176 voters, find the population of the city. 26. A city lot was sold for $1,883, which was 18% more than it cost. Find the cost of the lot. (12) 27. 4,186 is 15% more than what number? 28. A clerk whose salary was increased 11% re- ceived $1,082.25. How 1 much did he receive before the increase? 29. During the month of December a merchant sold goods to the value of $12,620.02 which was 9% more than his sales in November. What did his sales amount to in November? 30. After spending 35% of his money James had $735 left. How much had he at first? 31. What was the amount of a creditor's claim, who after collecting 37V 2 % of it, lost the remainder, $1250? 32. A government clerk spent 24% of his yearly sal- ary and had $1,520 left. Find the amount of his yearly salary. 33. I spent 8% of $2,500 for clothing and 10% of the remainder for provisions. How much did I spend in all? 34. A clerk's salary was increased 18%. He then re- ceived $1,652 a year. What was his salary before the increase? 35. I paid $1,250 for my automobile, or 60% more than for my horse and carriage. How much did my horse and carriage cost? 36. The cost of living for a family one year was $1,092, which was an increase of 4% over the cost of the year before. Find the cost for the year before. 37. The circulation of a publication has increased 25% in two years and is at present 138,125. What was the circulation two years ago? 38. A broker gained 17% by selling a quantity of grain for $1,894,23. What did he pay for the grain? 39. A horse and wagon are valued together at $225, and the horse is valued at 25% more than the wagon. What is the value of the horse? 40. An agent makes 20% by selling a book for $1.44, (13) If he had sold it for $2, how much would he have gained by selling 4 dozen books? 41. A dealer sold 10% of his stock of sugar, and then 33V3% of the remainder, after which he had 3,120 Ib. left. How much sugar had he at first? 42. Mr. Mahon had- 76% of his money invested in houses, and the rest, $7,680, he put in the bank. How much money had he? 43. If cloth shrinks 5%7c of its length in being sponged, find the original length of a sponged piece 37.8 yards long. 44. For what price per pair must shoes be sold to gain 25%, if 15% is lost when they are sold at $2.55? 45. A town has to raise $64,000 for expenses, which is 20% less than the amount required the year before. Find the amount required the year before? 46. Mr. Clark traveled 3,500 miles in an automobile. This distance is 30% less than the distance traveled by Mr. Harvey. How far did Mr. Harvey travel? 47. $3,300 equals 25% more than A's money,_and 25% less than B's money. How much more has B. than A.? 48. Mr. Gray has 86 acres in almonds and 26 acres in pears. 30% of his land is not tillable. Find his total acreage Exercise 9. To Supplement Pags 179-183. Find what per cent of: 1. 750 is 300. 7. 1,000 is 250. 2. 150 is 12. 8. 2,000 is 250. 3. 1325 is 165.625. 9. 2500 is 1250. 4. 2200 is 550. 10. 950 is 760. 5. 400 is 52. 11. 16500 is 7755. 6. 197'/2 is 39V 2 . 12. 575 is 120.75. (14) 13. 120.75 is 144.90 33. 360 mi. is 300 mi. 14. 220 is 308 34. 184 qt. is 5% gal. 15. 1242.50 is 24.85 35. 385 ft. is 161.7 ft. 16. 7,500 is 93.75 36. $530 is $257.05 17. 843 is 1,124 37. $4,086 is $3,268.80 18. 150 is 72 38. % is % 19. 380 is 95 39. 15-16 is 9-10 20. 728 is 4.55 40. .64 is .12 21. 5.82 is 1.94 41. .48 i3 .08 22. 2.50 is 4.05 4-2. 1472 is 460 23. 2,160 is 54 43. 460 is 1472 24. 77.25 is 6.18 25. 48.32 is 3.02 What per cent is: 26. 50.94 is 84.90 44. 23.1 of 165 27. 85.36 is 10.67 45. 64.89 of 927 28. $450 is $90 46. 26.79 of 893 29. 180 days is 60 days. 47. 46 of 276 30. $130 is $19.50 4-8. 35 of 175 31. $4,600 is $575 49. 157.08 of 374 32. 365 bu. is 146 bu. 50. 42.38 of 978 Exercise 10. To Supplement Pages 18M91. 1. A man sold a horse at a loss of 1% of the cost. If the actual loss was $43.40, find the cost. 2. A merchant sold a piano for $350 which cost him $280. What was the gain and the gain per cent? 3. An agent received $420 for selling a house. If the house was sold for $10,500, what was the rate of com- mission? 4. An agent received $420 for selling 4,800 tons of coal at $3.50 a ton. What was his charge per cent on the sum received for coal? 5. An agent charged $162.50 for selling a house. If the house was sold for $6,500, what was his charge per cent? (15) 6. I bought a phonograph for $50 and sold it at a loss of 347r. How much did I lose? 7. A grocer paid $14.40 for a tub of butter weighing 60 Ib. Find his selling price per pound if he gained 8. A quantity of leather that cost $1,648 was sold at a gain of 12%%. For how much was it sold? 9. A stationer bought blank note books at $1.08 per dozen and sold them at 15c each. What per cent did he gain? 10. A merchant sold shirts at $1.50 each, thereby gaining 20%. How much did he pay for them per dozen? 11. Find the gain per cent on a gross of brooms bought at $34.56 and sold at 28c each. 12. Find the cost per dozen pair of infants' woolen hose that retail for 25c a pair at a gain of 60%. 13. A man who paid $8,250 for a yacht sold it at a loss *of 14%. What was the selling price? 14. A lumber merchant sold 4,800 feet of lumber for $103.68, gaining 8%. How much did it cost him per thous- and feet? 15. Codfish bought for $3.50 per cwt. was sold in 5 pound boxes at 21c a box. Find the gain per cent. 16. A grocer bought a quantity of sugar at $4.50 per cwt. and sold it at a gain of 11 1-9%. What was his sell- ing price per pound? 17. Find the gain per cent on neckties bought at $1.32 per dozen and sold for 25c each. 18. A man bought a ring for $35, which was 12%% less than its value. He sold it for 12%% more than its value. Find the gain. 19. Shoes that cost $18.48 per dozen pairs were sold at $2 per pair. Find the per cent of gain. (16) 20. Mr. Barry bought two houses, one for $2,400 and the other for $5,200. He sold the first at 120% of the cost and on the second he lost 4%. Find the net gain on both transactions. 21. A dealer gained 20% on flour that he sold for $6 a barrel. The market advanced, and he sold the rest for $6.50 a barrel. What was his per cent of gain after the advance? 22. A merchant's complete stock of goods cost $50,000. He sold it at an average advance of 15% above cost and lost 2*4% of his sales in bad debts. Find the gain. 23. A wholesale fruit dealer paid $350 for oranges, $280 for bananas and $320 for peaches. He sold the oranges at cost, the bananas at 130% of the cost, and the peaches at a loss of 5%. Did he lose or gain on all and how much? 24. A and B formed a partnership. A put in $6,400 and B put in $4,500. What per cent of the whole was B's share? 25. The number of children of school age in a certain city was 18,500. 14,200 attended school. The number of pupils not attending school was what per cent of the en- tire number of children? 26. By selling goods for $1,173.92 a merchant gains $153.12. Find the gain per cent. 27. A real estate dealer bought a house for $72,500 and another one for $58,650. He then sold them both for $175,000. What was the gain per cent? 28. A merchant sold 154 yd. of material for $355. If he paid $1.75 per yard for the goods, what per cent did he gain? 29. A man earning $2,400 a year spends $1,600. What per cent of his income does he save? 30. A house that cost $5,000 was sold for $3,750. The selling price was what per cent of the cost? (17) 31. A man owned 1250 acres of land. 975. acres were under cultivation. What per cent of the land was un- cultivated ? 32. What rate of interest does a man pay if he pay $60 for the use of $1,200 for one year? 33. A man received $40 for selling a bill of goods amounting to $1,200. Find the rate of commission. 34. The yearly income from property that cost $27,- 200 was $12,650. The taxes and repairs amounted to $855. What per cent profit did the owner realize on his prop- erty? 35. A man insured his stock of goods for $25,000. The premium was $410. What was the rate of insurance? 36. What is my annual rate of income on $1,905 invested in real estate which rents for $15 a month, if I pay $27.60 for taxes and repairs? 37. A merchant bought 8 houses for $40,000 and sold them for $6,000 apiece. Find the gain per cent. 38. The base is 25.8; the percentage is 2.58; what is the per cent? 39. The assets of a firm are $20,280 and the liabilities are $24,000. What per cent of its debts can the firm pay? 40. How much per acre did a man receive for his land by selling 12y 2 % of 168 acres for $1,155? 41. I own % of a vessel and sell 50% of it; how much have I left? 42. The base is 3894; the per cent is 76; what is the percentage? 43. A man withdrew from the bank_33%% of his de- posits to pay a note of $200. How much remained in the bank. 44. I bought 152 yd. of muslin and sold 19 yd. of it. What per cent of it did I sell? (18) 45. A dealer put up 8,000 T. of ice. During' the sum- mer 15% of it melted and he sold 65% of the remainder; what per cent of the whole amount did he still have? 46. If by selling muslin at a profit of 12^%, a merchant gains $500, what did the muslin cost? 47. I owed A $1,450. I paid him 40% of it at one time, 20% of the remainder at another time, and 10% of what remained at another time; how much did I then owe him? 48. Harry Ammon invested $8,450 in real estate, which was 42*4% of the value of his property. What is the value of his property? 49. What per cent does a man make on his money, who rents a house that costs him $7,500, for $600 a year?' 50. In a battle in which 9,000 men were engaged, 2,000 men were killed; what per cent of the number en- gaged was not killed? 51. The approximate area of the land on the earth's surface is 50,000,000 sq. mi. which is 33V3% of the area of water. What is the area of the entire earth's sur- face? 52. A commission merchant received $52.25 for sell- ing flour at a commission of 2%. How much should he remit to the miller? 53. George White bought a house and lot for $4,500-. He paid 60% of it in cash and gave a mortgage for the remainder; for what amount did he give the mortgage? 54. A has $50 and B has $60. How many per cent less is A's money than B's? How many per cent more is B's money than A's? 55. A carpenter withdrew 25% of his money from the bank and paid 20% of it or $350, for lumber. How much had he in the bank? 56. $182.21 is what per cent of $650.75? 57. A merchant sold goods for $339.68 at a loss of 12%. What would have been his gain per cent if he had sold them for $432.32. (19) 58. A man's income is $1,500 a year and his expenses for the same time are $1,095. What per cent of his income does he save? 59. A man sold two horses for $150 each, gaining 20% on one and losing 20% on the other. Did he gain or lose by the two transactions, and how much? 60. I paid George $450, which was 12Mj% more than I still owed him; how much did I still owe him? 61. What number decreased by I2y 2 f /c of itself equals 770? 62. An agent sold a house and lot for $11,002.50, which was 12%% more than it cost him. What did it cost Him? 63. A certain man owns two farms. The first farm contains 290 acres, which is 42% smaller than the second; how many acres does the second farm contain? 64. Paid $3,360 for 40 mules. At how much per head must I sell them to gain 25% on the cost? 65. A man bought a farm of 160 acres for $12,800, and sold 90 acres of it for $6,300. What was the per cent of loss en the part sold? 66. A speculator had $16,800 in bank and withdrew of it to invest in wool at 21 cts. a pound. How many pounds did he buy? 67. I spent 8% of $2,500 for clothing and 10% of the remainder for provisions. How much did I spend in all? 68. A man bequeathed to his son 25% of $17,000, to his daughter 30% of the remainder, and the rest to his wife. What was his wife's share? 69. A collector whose fee was 4%, returned to his principal $540.96, what sum did he collect? 70. A capitalist invested 33% of his money in stock and had $33,299 left. How much money had he at first? (20) 71. A speculator who is worth $110,200 has 43% of his wealth in real estate and the remainder in bonds. How much has he in bonds? 72. Sold a horse and carriage for $270. If I receive 25% more for the carriage than for the horse, what sum did I receive for each? 73. A bankrupt settled with his creditors by paying them 623^% of the amount he owed them. What was the loss of the man to whom he owed $1,487.76? 74. Mr. Low had his money invested in three houses as follows: in the first $1,620, in the second $8,100, in the third $3,240. What per cent of his money was invest- ed in each house? 75. Mr. Jones' yearly income from a mine is $4,000, Which is 15% of the sum he invested in it. How much did he invest? 76. A store is rented for $60 a month. The yearly yearly rent is 8%9c of the value of the property. What is its value? 77. After Mr. Land has paid 37V 2 % of his debts, he found that $3,568 would pay the remainder. What was his total indebtedness? 78. Mr. Bingham sold two houses for $7,000 each; for the first he received I2y 2 f /f less than its value and for the second is 16%% more than its value. What was the value of each? 79. Mr. Allen bought for $3,200 a store which had depreciated 40% in value. What was the original value of the store? 80. When the Twentieth Century Novelty Company failed in business they had $3,350, which paid 67% of their debts. What was the amount of their debts? 81. A house worth $7,500 is damaged by fire $1,020. What is the rate per cent of the loss? (21) 82. If 22.9% of the cost of operating a mine in Alas- ka was for labor that cost $6434.90, find the cost of oper- ating the mine. 83. Mr. Williams' income from his "business in one year was $2,125, which was 25% of the value of his stock. The next year a fire damaged his stock to the extent of $1,275. What per cent of the value of his stock did he lose by fire? 84. A merchant had a stock of hats that cost $2.50 each. When he sold 75% of them, the cost value of the rest was $360. How many of these hats did he have in stock at first? 85. If a city decreased in population 15% each year for two successive years and then had 14,450 inhabitants, what was the population before the decrease? 86. Mr. Charles invested $6,540 n business, and a year later increased his capital 16%%. How much was his capital then? 87. Two years ago a lawyer's income was $4,868, but last year it decreased 12^%. What was his income last year? 88. If a house is sold for $6,400 at a gain of 14%, what per cent would have been gained by selling it 1'or $10,000? 89. Mr. Green buys a house and lot for $6,400. The average expenses per year for taxes are $80, for insur- ance $12, for repairs $24. What must be the annual rent, that he may have an income of 6% net oil the original cost of the property? 90. The discount on a bill is $127.50, the rate of dis- count 5%. Find the amount of goods bought. 91. I bought some property for $15,250, from which I receive an income of $150 per month. If I pay $56.40 for taxes and repairs, what is my annual net rate of in- come? (22) 92. A man drew 25% of his bank deposits and ex- pended 33M$% of the money thus drawn in the purchase of an automobile worth $3,500. How much money had he left in the bank? 93. I sold an article that cost $465 at a loss of 6%%. Find the loss and selling price. 94. A lawyer collected 25% of an account of $780, charging 4% commission. What was his commission and what sum should he pay his client? 95. A farm was bought for $12,500 and sold for $15,300. Find the gain or loss per cent. 96. A bankrupt sold his property for $6,200, which was 15% less than its real value. If the property had been sold for $8,250, what per cent above its real value would it have brought? 97. How much cash must I pay for a bill of library books invoiced at $400 at 25% discount and 4% off for cash? 98. A fence was built around a field 150 ft. long and 75 ft. wide. 11 1-9% of the fence was blown down by the wind. How much of the fence remained? 99. A boy sold his bicycle for $31.25, gaining 5% of the cost. How much did the bicycle cost him? 100. A man failed in business owing $24,000, and having assets $12,000. What per cent of his debts could he pay? How much would a creditor receive to whom he owed $1,785.50? COMMISSION Exercise 11. To Supplement Pages 192-193. 1. An agent collected a debt of $385.90, charging 4% commission. How much did he remit? (23) 2. What is a real estate agent's commission at 5% for renting a store for 1 year at $37 per month? 3. An agent collected $745 for his employer and charged 1% commission. Find the commission and the net proceeds. 4. A commission merchant purchased rice for me to the amount of $2,840.50. Find the commission at 3V 2 Vr. 5. Find the auctioneer's commission on the sale of rugs, the amount of the sale being $97,546.50, and the rate of commission 27. 6. Find the net proceeds from the sale of 250 bags of coffee, averaging 132 Ib. each, at 14%c per pound, reckon- ing the commission at 2%. 7. What is the weekly income of a clerk who re- ceives $8 a week and a commission of 4% of his sales, if his sales average $250 a week? 8. An agent sold 4 sewing machines at $35 each, receiving a commission of 40%. The expense of deliver- ing them was $2.25 each. Find the commission and the net proceeds. 9. A lawyer collected 807r of a debt of $2,500 and charged 107 commission. How much did the creditor receive? 10. A commission merchant sold 185 bbl. of apples at $5.25 a bbl. at a commission of 4 1 /9r. Find the amount of commission. 11. An agent received 3 1 / 49c commission for selling 90 boxes of shoes at $12.70 per box. What was his com- mission? 12. I sold $1,820 worth of goods for B, and charged him 3^7 for selling. Find the amount which was due him. 13. The invoice price of goods was $470, the agent's charges for buying were 5%%. Find the entire cost. (24) 14. I paid an agent $24.60 for selling a quantity of flour, at a commission of 4%. Find the amount of the sale. 15. What was the income last year of a commercial traveler whose sales amounted to $105,620, if his com- mission was 2%7f ? 16. An agent sells real estate for $19,225, receiving a commission of 5%. Find his commission. 17. How much business must a commission merchant do to earn $125, if his average commission is 2%9fc? 18. Find the rate of commission, if the net proceeds from a sale of $5,000 are $4,875. 19. The net proceeds of a sale of produce were $2,451. If the commission was $129, find the rate of commission. 20. If a lumber agent sold 80,000 feet of lumber at $24 per M. and received a commission of 4 1 / < 7r, how much did he receive for his services? 21. An agent bought a block of 14 houses, each house worth $3,200, on a commission of IW/c. How much did he receive for his services? 22. The rent of a house was $37.50 per month, and the agent retained out of that sum a commission of $1.50 per month. What was the rate of commission? 23. Find the architect's commission on an office build- ing that cost $24,000, if he received l%% for drawing the plans, and 3^7^ for superintending the construction? 24. A commercial traveler who sold goods on a com- mission had an income one year of $3,000 by selling goods to the amount of $120,000. W r hat was his rate of com- mission? 25. The commission at 3%9fc for selling a quantity of oats was $189. How many bushels were sold, if the price received was 30c per bushel? (25) 26. Mr. Ward sold a piano for $575, receiving a com- mission of 10% on the selling price. How much was his commission and how much money should he send to the owner of the piano? 27. Mr. Clark is an agent for the Elliott Piano Co., which pays him a commission of 25% on all his sales. During the month of January, 1917, he sold one piano at $325, one at $400, two at $250, and three at $200. How much were his commissions and how much should he return to the Elliott Piano Co.? 28. The expenses of his store for rent, heating, light- ing, advertising, clerk hire, etc., for January, were $178.50. How much did Mr. Clark make that month above ex- penses? 29. His living expenses for that month were $109.75. How much did he save? Would it be safe to reckon his yearly income on this basis? Why? 30. Mr. Adams sold a wagon for the Melvin Wagon Co. at $200, and after taking out his commission, sent the Wagon Co. $180. How much was his commission? What per cent of the value of the wagon? 31. Mr. Gordon buys chickens for a San Francisco firm, receiving a commission of 15% on all the money spent in buying them. If he buys $12,000 worth of chickens in a year, what is his income for that year? 32. An agent receives 32% commission on books. He has three styles of binding, cloth at $2.75, half morocco at $3.50, and morocco at $4.25. How much is his commission on each kind? 33. A real estate agent sells a farm of 360 acres at $44.60 an acre, receiving a commission of 5% on the first thousand dollars and 2^% commission on the remainder. Find his commission. 34. An agent buys an invoice of 89,500 Ib of coffee at 16c, 8% off for cash. What is his commission at 2%? (26) 35. How many barrels of flour at $3.50 ean an agent buy with $15,925 which sum includes his commission at 4%. Hint. Find cost of one barrel, including commission. 36. An agent bought 3,000 bu. of corn at 37^ cents, charging 2% commission and $8.75 insurance. For how much a bushel must it be sold to gain 20% over the entire cost? 37. A collector discounts a bill 15% and receives 5% commission on the amount collected. How much does the principal receive from a bill of $430.75. 38. An agent buys 12,000 bu. of potatoes, at 42 cents, commission 2 1 /%. He sells them at an advance of 28 4-7% on the cost price, charging 3% commission. Find both the commissions. 39. A dealer bought through his agent apples at $2.40 per barrel, allowing 2^% commission. How many barrels did he purchase if the cost and commission amounted to $312.42? How much was the commission? 40. My commission for selling furniture was $591.50; the net proceeds $16,308.50. What per cent did I charge for my services? INSURANCE. Exercise 12. To Supplement Pages 195-196. The rates given are the annual rates per $100 of in- surance. The rate for three years is double the annual rate. Find the premiums on the following: Insurance. Rate. Term. 1. $1,350 $ .70 1 year. 2. $2,400 $ .65 3 years 3. $4,600 $1.37 1 year 4. $6,000 $ .95 1 year 5. $5,540 $1.25 1 year (27) 3 years 3 years 1 year 3 years 1 year Premium. $22.50 $30.00 $24.00 $8.125 $33.40 $22.80 $105.60 $57.75 $46.38 $244.80 Premium $68.75 $88.20 $50.31 $315 $208.50 $87.50 $97.20 $35.25 $21.645 $185.50 31. Mr. Morton takes out an insurance policy of $1,500 on his house and $750 on his furniture for a term of three years. Rate of insurance $.60. What is the premium? 32. A stock of merchandise was insured for $2,700. Rate $1.35. Term 1 year. Find the premium. (28) 6. $1,890. $1.35 7. $22,700 $ .60 8. $8,210 $2.25 9. $10,300 $1.10 10. $2,720 $1.50 Find the rate of insurance: Insurance. Term. 11. $1,000 1 year 12. $2,000 1 year 13. $800 3 years 14. $650 1 year 15. $2,000 1 year 16. $1,900 3 years 17. $4,000 3 years 18. $1,650 3 years 19. $3,865 1 year 20. $14,400 3 years Find the amount of insurance: Term. Kate 21. 1 year $1.25 22. 1 year $1.05 23. 1 year $1.72 24. 3 years $ .70 25. 1 year $1.39 26. 1 year $1.75 27. 1 year $ .90 28. 1 year $ .75 29. 1 year $1.30 30. 1 year $2.65 33. A man insured his property for three years as fol- lows: house $300, rate $.60; furniture $200, rate $.60; barn $50, rate $1.25. Find the total premium. 34. What premium will be paid on the following in- surance for one year: building $10,000. rate $1.65, furni- ture and fixtures $350, rate $2.15; stock of merchandise $2,250, rate $2.15? 35. Mr. Black's stock of jewelry was insured for $2,500 for three years. If the rate is $1.57, find the premium. 36. The premium for insuring a stock of drugs for one year at $3.65 is $109.50. Find the face of the policy. 37. Property worth $13,500 was insured for three years for % of its value at $1.67. Find the premium. 38. The cost of insurance for 3 years on a dwelling was $24.00. Find the annual rate if the face of the policy was $1,600. 39. Mr. Nelson insured his house for three years at the rate of $1.32 per $100. The premium was $88.44. Find the amount of insurance. 40. The premium on $7,500 isurance for three years was $220.50. Find the annual premium. TAXES Exercise 13. To Supplement Pages 198-201. At the rate of $1.70 on the hundred, 1. Find the tax on $5,000. 2. Find the tax on $800. 3. Find the tax on $380. 4. Find the tax on $469. 5. Find the tax on $97. 6. Find the tax on $3,469. 7. Find the tax on $937. (29) 8. Find the tax on $3,248. 9. Find the tax on $18,345. 10. Find the tax on $39,846. 11. The tax rate is $1.40 on the $100.00. Mr. Brown's tax is $54.64. On how much property does he paj tax if his poll tax is $2.00? 12. How many dollars on $100 must be levied om $486,500, to raise $5,838 tax? 13. What is .the tax on $6,500 at $2.62 on the $100? 14. The rate of taxation being $1.50 on the $100, how much must the company pay whose property is assessed at $75,000? 15. A town has an assessed valuation of $4,500,000, and it has to raise $24,750 by taxation. What is the rate? 16. The rate of taxation being $.75 on the $100, how much tax must a man pay on $8,500, together with $1 poll tax? 17. The assessed valuation of property in a town is $2,520,000 and the tax rate is $2.35 on the $100. What is Mr. Smith's tax if his property is assesed at $21,500? What is the total tax of the town? 18. A town has an assessed valuation of $720,000, and it wishes to levy a tax of $5,400 for highways and schools. What must be the rate on the $100? 19. What is the total tax of a man whose property is assessed at $8,400, the rate being 1 mill for state pur- poses, three mills for county purposes, % mill for town, and two mills for school purposes, together with $1 poll tax? Given the following assessed valuations and tax levies, find the rates of taxation on the $100: 20. $4,200,000, $16,800 21. $3,700,000, $20,350 (30) 22. $9,250,000, $41,625 24. $7,875,000, $23,625 23. $2,900,000, $8,700 25. $14,500,000, $87,000 Given the following tax levies and rates of taxation, find the assessed valuation: 26. $13,750, 5 mills. 28. $21,000, 6 mills. 27. $57,750. 7 mills. 29. $73,000, 8 mills. Find the tax at $.55 on the $100 on: 30. $6,500 36. $4,875 31. $12,000 37. $24,400 32. $31,100 38. $18,875 33. $8,750 39. $7,675 34. $16,500 40. $23,500 35. $23,250 41. $45,250 42. The taxable value of the property in a town is $675,000, and the rate of taxation is $.70 on the 100 dollars, what is the tax? 43. Find Mr. Wilson's tax, the assessed value of whose real estate is $13,680, and personal property $7,360, at the rate of $.55 on the 100 dollars. 44. At the rate of $.90 on the 100 dollars what must be the assessed value of property to yield $38,520 tax? 45. The assessed value of the property of a town is $192,000. What must be the rate in order to raise $1,536 tax? 46. How much tax will that man pay whose property is valued at $25,780, the rate being $.75 on the $100 and his income $2,500 being taxed at %%. 47. A company pays a tax of $4,875, at the rate of $.75 on the $100. What is the asessed value of the prop- erty? 48. The assessed valuation of a school district was $246,750; the tax rate was 8 mills on a dollar. How much was left for school purposes, if the collector received 3% of the amount collected? (31) 49. In a town $8,500 tax was levied; 4% was un- collectable, and the collector's fee was 2 1 / 2 % of the amount collected. How much was left for the town? 50. How many mills on a dollar must be levied to raise a net tax of $16,005 on an assessed valuation of one and a half millions, allowing 3% for collecting? TRADE DISCOUNT. Exercise 14. To Suplement Pages 204-205. In each of the following, find the net amount from the given gross amount and discounts: 1. $200; 20%, 5% 1. $230; 5%, 2% 2. $400; 25%, 10% 8. $498; 16%%, 4% 3. $600; 10%, 10% 9. $560; 37V 2 %, 15% 4. $300; 15%, 20% 10. $744; 12V 2 %, 33V 3 % 5. $720; 50%, 10% 11. $1,000; 10%, 10%, 5% 6. $850; 12%, 18% 12. $2,400; 25%, 20%, 8% 13. Find the discount at 14% on $8.50. 14. Find the discount at 8% on a coat marked $18.75. 15. A bicycle was marked at $87.50; the dealer sold it at a discount of 12%. How much was the discount? How much did he receive for it? 16. What is the cash value of a bill amounting to $4,280 at 15% discount and 2y 2 % off for cash? 17. The catalog price of a lot of books is $960; what does the dealer pay for them at 33V 3 and 8V3% off? 18. Find the net price of a bill of hardware sold at a discount of 20, 10 and 5% off, the gross price being $1,280.40. 19." What is the difference between a discount of 35% on a bill of $320, and two successive discounts of 20% and 15% ? (32) 20. Cooper & Son received discounts of 40% and 10% on a bill of $350 for silver plate. Find the total discount. 21. A bill of school supplies amounted to $475.50. What was the cash payment if there was a discount of 33V 3 % and 5% for cash? 22. Prom a bill of $840 for window glass 90% and 10% discounts were allowed. What was the net amount of the bill? 23. Find the total discount on a bill of goods amount- ing to $1,280, with discounts of 12^% and 30%. 24. W 7 hat is the amount of a bill of $496 for tinware if the discounts are 75%, 10%, and 5% for cash? 25. A man sold a bill of goods amounting to $840, at a discount of 12^% for cash. What \vas the discount? 26. I bought pocket knives listed at $1.50 each, at 50 and 8% off. How much did they cost me? 27. I purchased 150 yd. of carpet, the list price being 80c a yard, at 15 and 10% off, an additional discount of 5% being allowed me for cash. How much did the carpet cost me per yard? 28. My agent bought a bill of hardware for me at 30 and 49<: off the list price and charged me 5% for buying, My entire bill was $529.20. What would have been the amount of my bill had the goods been purchased at list price? 29. I bought shovels at a discount of 20 and the list price being $1.25 apiece. How many shovels were bought if the discount amounted to $112.50. 30. The amount of discount at 10 and 5% off is $43.50. Find the gross amount of the bill? 31. A piano was listed at $675. If sold at 35% dis- count, what was the selling price? 32. What is paid for a pane of glass listed at $1.20 and sold at 25% and 10% off. (33) 33. A gross of cartridges is listed at $3.50 and sold at 14 2-7 and 8% discount. Find the price paid. 34. An agent sold a $3.50 book at 20% discount. What did he receive for it? 35. A man bought a bill of goods amounting to $468 ; the merchant discounted the bill for 4% cash. How much was paid? 36. How much is paid for a dozen books if the list price is $8.40 and the discounts are 25 and 10%? 37. Find the net amount of a bill of $289.20, subject to 25, 15 and 12^% off. 38. The gross amount of a bill of goods was $891, and the discounts were 25 and 15%. Find the net amount. 39. Find the difference between a single discount of 50% off and two successive discounts of 25% and 25% off a bill of $1,000. 40. An agent bought 25 sewing machines with 25, 10, and 10% off the list price of $40 each, and sold them at 10% advance of the list price. Find his whole gain. 41. A merchant buys goods amounting by list price to $722.40. He gets 25 and 10% off, and sold them at a 5% advance on the list price. Find his whole gain. REVIEW OF TRADE DISCOUNT, COMMISSION, INSURANCE AND TAXES. Exercise 15. 1. If land' was sold for $85,000 and the real estate agent charged 6% for selling, what was the commission and the proceeds? 2. An agent received $708.75 for selling property for $15,750. Find the rate of commission. 3. The assessed valuation of property in a county is $22,750,000. The county expenses for a year are $523,250. Find the rate of taxation. Mr. B's property is assessed for $3,462; what tax does he pay? ' (34) 4. A merchant buys goods listed at $2,911.50. If discounts of 80, 20, 25% are allowed, find the net amount of the bill and the discount. 5. A ship owner paid $690 at 1%% for insuring % the value of his ship. What was the value of his ship? 6. The total cost of a church was $12,646.40 which includes the architect's commission, $296.40. Find the per cent of commission. 7. Bought 75 carpet sweepers at $2.40 each, less 25, 20, and 10%; sold them at the same price, less 20, 15, and 10%; what was my profit? 8. The cost is $275 ; profit 20%. Find the selling price. 9. The selling price is $812; profit 12%. What is the cost? 10. List ( price $1,700; discounts, 33%., 16%, 20%. W T hat is the net price? 11. Profit 12%%; selling price $16,114.95. What is the cost and profit? 12. A merchant insured a stock of goods worth $4,500 for % of its value at 2%%. What was the premium? 13. A has $1,240 worth of machinery insured at %%; store worth $5,200 insured at ! 1 /4%; stock of merchandise worth $2,700 insured at 8-9%. How much premium does he pay? 14. Jones paid $104.95 premium for insurance on his property for % of its value at $2.20. What was the value of his property? 15. Cost, $1,575.40; selling price, $1,732.94. Find the gain per cent. 16. If a book dealer buys books at a discount of 33%% from the list price and sells them at the list price, what per cent does he make? 17. Paid $56.25 for selling grain at %% commission. Find the net proceeds. (35) 18. A corporation has a capital of $360,000; the gross receipts are $62,120; the expenses are $32,350. What per cent of dividends can be declared after reserving a sur- plus of $5,650? 19. The list price of an article with three different houses is $400. One house offers discounts of 20, 10, and 5%; the second 5, 10, and 20%; the third 10, 5, and 20%. Which is the best offer and why? 20. On a bill of $1,025, what is the difference between discounts of 40, 20 and 25%, and a straight discount of 85%? INTEREST. Exercise 16. To Supplement Pages 207-211. Find the interest on: 1. $730 for 2 years at 4%. 2. $962 for 5 years at 6%. 3. $625 for 2% years at 8%. 4. $350 for 3y 2 years at 7%. 5. $125 for 2 years 8 months at 6%. 6. $333 for 4 years 10 months at 5%. 7. $560 for 3 years 4 months at 5%. 8. $426 for 1 year 7 months at 6%. 9. $26.40 for 9 months at T/c. 10. $402 for 3 years 4 months at 6%. 11. $521 for 2 years 4 months at 4 1 /7 12. $325 for 2 years 5 months at 5%. 13. $650 for 1 year 9 months at 3V 2 %. 14. $462 for 2 years 7 months at 6%. 15. $320 for 8 months at 6%. 16. $175 for 9 months at 6%. 17. $330 for 7 months at 89c. 18. $240 for 7 months at 5%. (36) 19. $185 for 2 years 6 months at 59t. 20. $240 for 3 years 8 months 2 days at 47c. 21. $1,200 for 2 years 6 months 3 days at 3%. 22. $475 for 2 years 2 months 2 days at 4 1 /7f. 23. $2,435 for 2 years 3 months 9 days at 4'r. 24. $1,765 for 3 years 2 months 5 days at 4%9fc. 25. $4,200 for 1 year 3 months 15 days at 5 r A. 26. $381.25 for 1 year 6 months 18 days at 3%. 27. $426.40 for 1 year 6 months 20 days at 59c. 28. $692.50 for 2 years 8 months 15 days at Find the amount of: 29. $175 for 1 year 2 months 6 days at 69c. 30. $342 for 2 years 3 months 4 days at 5%. 31. $1,725 for 2 years 8 months 6 days at 32. $2,175 for 3 years 6 months 15 days at 59c. 33. $312.50 for 2 years 7 months 10 days at 4%. 34. $427.25 for 1 year 8 months 3 days at 35. $375.50 for 2 years 6 months 4 days at 36. $137.50 for 1 year 7 months 2 days at 37. A man can buy $1,750 worth of goods on 90 days credit, or he can get them for $1,720 cash, which he can borrow for 90 days at 69c. Which is the better plan and how much better is it? 38. Find the amount of $524.36 on interest for 2 years 5 months 18 days at 7%. 39.. $60.24 for 2 years 4 months 15 days at 5%. 40. $45.48 for 3 years 5 months 10 days at 6%. 41. $2,800 for 2 years 6 months 15 days at 4%. 42. $5,000 for 3 years 8 months 11 days at 6%. 43. $468.36 for 3 years 9 months 10 days at 4'r. 44. $25,000 for 2 years 5 months 12 days at Q7c. 45. $68,400 for 1 year 1 month 21 days at 7' ' '< . 46. $297.45 for 2 years 3 months 15 days at 6>. (37) 47. $634.75 for 3 years 6 months 9 days at 8%. 48. $1,500 on interest from Sept 7, 1906 to Dec. 31, 1908, at 4%. INTEREST "60-DAY METHOD" Exercise 17. To Supplement Page 212. At 6% find the interest on: 1. $1,293.50 for 60 days. 2. $175.40 for 30 days. 3. $2,740.25 for 15 days. 4. $625 for 4 months. 5. $330.80 for 90 days. 6. $1,218.60 for 40 days. 7. $65.50 for 50 days. 8. $187.50 for 70 days. 9. $8,932 for 80 days. 10. $531.90 for 75 days. 11. $36.45 for 45 days. 12. $277.75 for 20 days. 13. $624.60 for 12 days. 14. $355.70 for 2 months 10 days. 15. $3,200 for 4 months 15 days. 16. $450.35 for 96 days. 17. $485 for 63 days. 18. $120.60 for 66 days. 19. $1,679 for 86 days. 20. $1,580.50. for 76 days. Find the interest for 60 days on: 21. $350 at 5%. 22. $1,570.20 at 4%. 23. $5,460 at 2%. 24. $328.45 at 8%. 25. $9,346.25 at 9%. (38) 26. $132 at 7%. 27. $12,450.50 at 4V 2 %. 28. $675.20 at iy 2 %. 29. $97.35 at 3%. Find the interest on: 30. $780 at 3% for 90 days. 31. $960 at 8% for 80 days. 32. $136.75 at 7% for 1 month 15 days. 33. $605 at 5% for 2 months 10 days. 34. $1,200 at 2% for 2 months 15 days. 35. $1,000.25 at 9% for 50 days. 36. $600 at 7V 2 % for 35 days. 37. $1,900 at 41/2% for 1 month 12 days. 38. $2,544 at 5%% for 48 days. 39. $3,580.50 at 4% for 96 days. 40. $45.45 at 8% for 66 days. 41. $1,800 at 9% for 2 months 9 days. 42. $375 at 7% for 2 months 8 days. 43. $175.20 at 3% for 4 months 15 days. 44. $1,225 at 6% for 2 months 12 days. 45. $900.45 at 5% for 75 days. 46. $214.45 at 1% for 48 days. 47. $240.60 at 2%% for 40 days. 48. $5,000 at 3^% for 3 months 9 days. 49. $10,500 at 6%% for 26 days. 50. $865.20 for 93 days at 5%. 51.' $265.50 for 120 days at 8%. 52. $840 for 75 days at 4%. 53. $1,740 for 45 days at 9%.. 54. $1,250 for 48 days at 7%. 55. $520 for 72 days at 5%. 56. $384.25 for 36 days at 4%%. 57. $250 for 40 days at 7%%. 58. $1,825 for 6 days at 8^c. (39) 59. $127.30 for 8 days at 3%. 60. $416.25 for 5 days at 5%%. 61. $580 for 33 days at 7%. 62. $184.60 for 36 days at 5%. 63. $465.30 for 27 days at 8%. 64. $416 for 33 days at 7%. INTEREST "CANCELLATION METHOD." Exercise 18. To Supplement Page 216. Find interest on: 1. $480 at 6% for 8 months. 2. $720 at 5% for 9 months 10 days. 3. $1,250 at 6% for 2 years 6 months 6 days. 4. $160 at 6% for 1 year 9 months 18 days. 5. $320 at 5% for 2 years 4 months 20 days. 6. $440 at 7% for 3 years 1 month 15 days. 7. $400 at 9% for 1 year 2 months 28 days. 8. $750 at 8 % for 11 months 16 days. 9. $1,264.80 at 6% for 42 days. 10. $225 at 1% for 108 days. 11. $1,140 at 7% for 11 months 20 days. 12. $1,000 at 51/2% for 2 months 27 days. PARTIAL PAYMENTS. MERCHANT'S RULE. Exercise 19. Page 216. Find the balance at the date of settlement, allowing 6% interest: 1. Note of $875, April 1. Indorsements: $300, May 1; $125, June 15; $275, July 25. Settled Nov. 20. 2. Note of $250, February 1. Indorsements: $30, March 1; $70, May 15; $50, July 10. Settled September 15. (40) 3. Note of $750 March 1. Indorsements: May 10, $100; July 12, $75; Sept. 4, $40. Settled Oct. 15. Find the amount paid at settlement: 4. Face of note, $80. Date Nov. 5, 1911. Rate 1%. Indorsed, $30, Dec. 5, 1911. Jan. 5, 1912, $25. Settled Feb. 5, 1912. 5. Face of note $120. Date Aug. 9, 1911. Rate 6%. Indorsed, Sept. 15, 1911, $48. Oct. 1, 1911, $45. Settled Oct. 9, 1911. 6. Face of note, $60. Date. June 20, 1911. Rate 8%. Indorsed, $20, July 6, 1911. Settled Aug. 23, 1911. Find balance due: 7. Note of $230. Date, May 9, 1911. Settlement Feb. 24, 1912. Payments: $40, July 1, 1911; $75, Sept. 16, 1911; $50, Jan. 2, 1912; Rate of interest 6#. 8. Note of $375 given March 3, 1912. Payments: $30, May 8, 1912; $65, Aug. 16, 1912; $110, Nov. 20, 1912. Rate of interest 59r. Settlement Jan. 1, 1913. 9. Note of $600 given May 16, 1912, bearing in- terest at 5v/. Payments: $50, June 1; $25, July 3; $50, July 10. Settlement Nov. 12, 1912. Find balance due. 10. Feb. 1, 1912, Mr. Rogers bought a lot costing $1,400. He paid $200 cash and agreed to pay the balance in installments $150 on the first of each month, with interest at 69r. Find the amount of interest paid each time and the total cost of the lot. 11. I had a note for $2,000, date April 1, 1912, on which the following payments were indorsed: June 25, $450; Aug. 16, $800; Nov. 10, $600; Jan 1, 1913, $150. How much was due April 1, 1913, interest 69c. 12. A note for $884, dated Jan. 15, 1911, had indorsed on it the following payments: Feb. 25, $100; May 10, $288; July 25, $260; Sept. 19, $150. Find the balance due Jan. 15, 1912, interest Q f /r. (41) 13. A note for $6,840, date May 15, 1912, bears in- dorsements as follows: July 21, $300; Oct. 10, $500; Feb. 24, 1913, $200. Find the balance due May 15, 1913, inter- est 6%. 14. A note for $100 made Jan. 1, has the following payments indorsed: March 1, $10; April 1, $25. Find the balance July 1, allowing 6% interest. PAKTIAL PAYMENTS. UNITED STATES KULE. Exercise 20. To Supplement Page 216. 1. On a note dated January 1, 1911, for $300 bearing 6Vc interest, the following payment was made: Jan. 1, 1912, $70. What was due Jan. 1, 1913. 2. Note of $980. Dated July 5, 1908. Rate of in- terest 8 %. Payments March 7, 1909, $170; Jan. 5, 1910, $25; April 20, 1911, $320. What was due July 5, 1912? 3. A note for $375, at 5%, has a payment of $18.75 indorsed annually at the close of each year from its date, for three years. How much is due at the end of the fourth year? 4. A note of $600, dated May 1, 1911. Interest 6%. Payments: August 12, 1911, $75; July 24, 1912, $200. What was due May 1, 1913? 5. A note for $500, at 6%, is dated January 1, 1908 and has the following partial payments indorsed: July 2, 1908, $100; January 1, 1909, $100. How much is due July 1, 1909? 6. A note of $300 at 6%, is dated April 1, 1910, and has the following partial payments indorsed: Sept. 1, 1910, $50; Feb. 16, 1911, $75; Jan. 1, 1912, $100. How much is due July 1, 1912? 7. A note for $1,800 at 5%, dated April 16, 1910, has the following partial payments indorsed: July 2, 1910, $500; Oct. 1, 1910, $250; Feb. 1, 1911, $100; May 1, 1911, $375. How much is due Sept. 5, 1911? 8. A note for $750, at 4%, is dated June 15, 1910, and has the following partial payments indorsed: March 6, 1911, $200; Sept. 6, 1911, $150; Jan. 17, 1912, $250. How much is due on the day of settlement, May 14, 1912? (42) 9. A note for $600, at 5 C , is dated July 2, 1910, and has the following partial payments indorsed: Jan. 2, 1911, $50; Feb. 11, 1911, $75; July 8, 1911, $200; Sept. 10, 1911, $80; Nov. 2, 1911, $50. How much is due Jan. 2, 1912? 10. A note for $1,200 at 4%, dated May 1, 1910, has the following partial payments indorsed: July 2, 1910, by labor $5; July 9, 1910, by labor, $2; Sept. 1, 1910, $93; May 1, 1911, $450; November 1, 1911, $500. How much is due Jan. 1, 1912. BANK DISCOUNT. Exercise 21. To Supplement Pages 218-219. Find the discount and proceeds: Note Time Kate 1. $625 60 da. 4% 2. $775 40 da. 6% 3. $4,625 70 da. 5% & $935.20 90 da. 7% 5. $440.75 80 da. 4V 2 % 6. 8,290 90 da. 9% 7. $760 63 da. 8% 8. $1,734.50 93 da. 7V 2 % 9. $894 75 da. 3% 10. $660.90 72 da. 6% 11. $1,820.45 45 da. 5% 12. $3,919.10 70 da. 12% 13. $375.75 80 da. 4 x /2% 14. $2,250 33 da. 4% 15. $1,875.80 66 da. 6% 16. $4,208.55 96 da. 7% 17. $710.75 . 80 da. 5% 18. $162.40 9 da. 9% 19. $287.60 76 da. 2% 20. $465.70 2 mo. 10 da, 6% 21. $9,492 2 mo. 15 da. 7%% 22. $1,248.60 2 mo. 6 da. 4% 23. $725.45 4 mo. da. 3% 24. $632.90 2 mo. 12 da. 5% 25. $2,471.80 2 mo. 20 da. 8% (43) BANK DISCOUNT. Exercise 22. To Supplement Pages 218-19. If the time is given in days, use exact time in finding the date of maturity. Otherwise use ordinary time. Al- ways use the exact time when finding the discount period. In these problems no days of grace are allowed. If the note is non-interest bearing, compute the discount on the face of the note. If interest bearing, compute the discount on the amount due at maturity. Find date of maturity, bank discount, and proceeds: 1. $480.00 Fresno, Cal., April 6, 1917. Ninety days after date I promise to pay to the order of Samuel D. Smith Four hundred eighty and no-100 Dollars, value received. R. L. POLK. Discounted May 25, 1917, at 7%. 2. $365.00 Oakland, Cal., March 2, 1917. Thirty days after date I promise to pay to the order of Harold A. Evans Three hundred sixty-five and no-100 Dollars, value received. HENRY SAVAGE. Discounted March 9, 1917, at 8%. 3. $785.00 Santa Rosa, Cal., Jan. 5, 1917 Seven months after date I promise to pay to the order of Francis H. Rowley ' Seven hundred eighty-five and no-100 Dollars, value received. RILEY W. SMITH. Discounted April 27, 1917, at 9%. 4. $1300.00 San Diego, Cal., Feb. 19, 1917. One year after date I promise to pay to the order of (44) Edward E. Fish One thousand three hundred and no-100 Dollars, value received. A. L. BENEDICT. Discounted August 23, 1917, at 6%. 5. $150.00 Prescott, Ariz., March 3, 1917. One year after date I promise to pay to the order of James L. Hill One hundred fifty and no-100 Dollars value received. WINTHROP PACKARD. Discounted April 8, 1917, at 7%7c. 6. $440.50 Portland, Ore., May 25, 1917. Six months after date I promise to pay to Albert Day or order Four hundred forty and 50-100 Dollars, value received. DAVID HOLMES. Discounted July 18, 1917, at 6%. 7. $768.00. Los Angeles, Cal., Sept. 27, 1917 Three months after date, for value received, I promise to pay to John Nelson or order Seven hundred sixty-eight and no-100 Dollars, N. J. NORTON. Discounted Oct. 12, 1917, at 7%. 8. Note of $575 dated Jan. 7, 1912, and due in 90 days with interest at 7%. Discounted Mar. 1, 1912, at 8%. 9. Note of $692.50 dated July 10, 1912, and due in 60 days from date. Interest 5%. Discounted July 29, 1912, at 7%. 10 $1,220.00 San Francisco, Cal., Sept. 1, 1916. Four months after date, for value received, I promise to pay to James E. Collan or order, Twelve hundred twenty and no-100 Dollars, with interest thereon at 6%. HARRY STANFORD. Discounted Nov. 12, 1916, at 7%. (45) 11. $2,000.00 Sacramento, Cal., Sept. 14, 1913. Eighty days after date I promise to pay to Charles Culver or order Two thousand and no-100 Dollars, with interest at the rate of 4^% per annum, for value re- ceived. THOMAS DREW. Discounted Oct. 3, 1913, at 6%. 12. $1,300.00 Oroville, Cal, June 19, 1913. Ninety days after date, for value received, I promise to pay to Grover Walker or order, Thirteen hundred and no-100 Dollars, with interest at 7% per cent per annum. JAMES GROSS. Discounted Aug. 21, 1913, at 8%. 13. $2,400.00 San Jose, Cal., Apr. 17, 1913. Forty days after date, for value received, I promise to pay to Arthur S. Coleman or order, Two thousand four hundred and no-100 Dolars, with interest at 5% per annum. LLOYD D. CARTER. Discounted Apr. 21, 1913, at 7%. 14. $540.00 Gridley, Cal., Aug. 16, 1913. Sixty days after date, for value received, I promise to pay to James Harver or order, Five hundred forty and no-100 Dollars, with interest at 1% per annum. ROY NUXX. Discounted Sept. 11, 1913, at 8%. 15. $700.00 Chico, Cal., Dec. 2, 1916. Four months after date, for value received, I promise to pay to Martha Jones or order Seven hundred and no-100 Dollars, with interest at 8% per annum. ROBERT W T OODY. Discounted Jan. 24, 1917, at 9%. (46) MEASUKEMENTS. Exercise 23. To Supplement Page 225. Reduce to inches: 1. 8 yd. 1 ft. 5 in. 2. 4 yd. 2 ft. 7 in. 3. 1 rd. 2 yd. 1 ft. 3 in. 4. 12 yd. 1 ft. 8 in. 5. 2 rd. 1 ft. 10 in. Reduce to feet: 6. 2 rd. 1 yd. 5 ft. 7. 1 mi. 1 rd. 1 yd. 1 ft. 8. 22 rd. 4 yd. 2 ft. 9. 109 rd. 5 yd. 1 ft. 6 in. 10. 225 rd. 3 yd. 2 ft. 8 in. Reduce to higher denominations and prove: 11. 6,602 ft. 12. 126,762 in. 13. 9,845 yd. 14. 33,784 in. 15. 19,480 rd. 16. 77,642 ft. 17. 16,222 ft. 18. 17,892 in. 19. 24,000 ft. 20. 12,768 yd. 21. 7,043 yd. 22. 31,415 ft. 23. 33,768 in. 24. 5,301 rd. 25. 43,735 ft. 26. Reduce 8 mi. 225 rd. to rods. 27. Reduce 16 mi. 25 rd. to rods. 28. Reduce 18 rd. 2 yd. 1 ft. 9 in. to inches. 29. Reduce 12,760 in. to higher denominations. Add: 30. 4 yd. 2 ft. 3 in., 5 yd. 1 ft. 9 in., 3 yd. 2 ft. 8 in. 31. 13 yd. 2 ft 11 in., 15 yd. 2 ft. 9 in., 18 yd. 2 ft. 10 in. 32. 15 yd. 1 ft. 7 in., 3 yd. 1 ft. 6 in., 12 yd. 2 ft. 5 in. 33. 12 mi. 25 rd. 5 yd., 25 mi. 12 rd. 4 yd., 37 mi. 13 rd. 3 yd., 16 mi. 31 rd. 4 yd. 34. 114 rd. 5 yd. 2 ft., 79 rd. 3 yd. 2 ft., 65 rd. 4 yd. 1 ft., 87 rd. 5 yd. 2 ft. 35. 7 mi. 230 rd. 9 ft, 92 mi., 164 rd. 15 ft., 46 mi. 189 rd. 14 ft., 23 mi. 207 rd. 8 ft. Subtract: 37. 27 rd. 3 ft. 1 in., 14 rd. 4 ft. 2 in. 37. 27 rd. 3 ft. lin., 14 rd. 4 ft. 2 in. 38. 173 rd. 4 ft. 1 in., 37 rd. 5 ft. 2 in. 39. 7 mi. 140 rd. 3 yd., 5 mi. 230 rd. 5 yd. 40. 13 mi. 35 rd. 11 ft., 11 mi. 57 rd. 15 ft. 41. 5 mi. 230 rd. 5 ft., 3 mi. 175 rd. 11 ft. Add: 42. 2 yd. 1 ft. Iiy 2 in., 5 yd. 1 ft. 2*4 in. 43." 6 yd. 2 ft. 7V 3 in., 3 yd. 2 ft. 11% .n. 44. 6 mi. 200 rd. 2 yd. 1 ft 10 in., 8 mi. 120 rd. 1 yd. 2 ft. 6 in. 45. 10 mi. ISO.rd. 4 yd. 2 ft. 3 in., 7 mi. 40 rd. 2 yd. 1 ft. 11 in. 46. 10 mi. 20 rd. 1 yd. 2 ft 10 in., 7 mi. 300 rd. 1 yd. 1 ft. 8 in. 47. 8 mi. 150 rd. 4 yd. 2 ft. 11 in., 4 mi. 100 rd. 1 yd. 1 ft. 5 in. 48. 16 mi. 200 rd. 3 yd. 2 ft. 4 in., 14 mi. 150 rd. 1 yd. 1 ft. 10 in. 49. 18 mi. 2 rd. 4 yd. 2 ft. 10 in., 5 -mi. 319 rd. 2 yd. 1 ft. 7 in. 50. 15 mi. 3 rd. 2 yd. 2 ft. 3 in., 10 mi. 319 rd. 1 yd. 1 ft. 9 in. (48) Exercise 24. To Supplement Pagre 225. 1. What is the cost of fencing a rectangular field 129 rd. 4 yd. long and 110 rd. 1% yd. wide at 90c a rod? 2. What is the cost of fencing a rectangular field 185% ft. long and 123 ^ ft. wide if the fence costs 50c a yard? 3. How many feet of molding will be required for the four walls of a room 18 ft. 4 in. long and 15 ft. 10 in. wide? 4. The sides of a triangular field are 197 ft., 256 11-12 ft. and 301% ft. What is the cost of the wire for fencing the field if the fence contains 4 wires and the wire costs % of a cent a yard? 5. Find the perimeter of a room 16 ft. 4 in. x 15 ft. 8 in. 6. The perimeter of a rectangle is 511 ft. 10 in., the width is 115 ft. 4 in. Find the length. 7. What is the perimeter of a square one side of which is 4 yd. 2 ft. 5 in? 8. Find the total number of feet of picture molding required for three rooms of the following dimensions: 12 ft. x 14 ft. 6 in.; 11 ft. 6 in. x 13 ft.; 14 ft. 4 in. x 15 ft. 6 in. Find the cost at 3 cents a foot. Find the total perimeter in feet and inches of rooms of the following dimensions: 9. 30 ft. 6 in. x 40 ft. 5 in., 16 ft 8 in. x 20 ft. 2 in. 25 ft. 3 in. x 30 ft. 7 in., 10 ft. 6 in. x 13 ft. 4 in. 10. 12 ft. x 14 ft., 10 ft. 9 in. x 11 ft. 8 in., 16 ft. x 17 ft. 6 in., 17 ft. 6 in. x 18 ft, 19 ft. x 20 ft. 11. 6 ft. 4 in. x 9 ft. 6 in., 69 ft. 6 in. x 80 ft. 7 in., 16 ft. 10 in. x 18 ft. 6 in., 20 ft. 2 in. x 25 ft. 4 in., 30 ft. 4 in. x 35 ft. 6 in., 28 ft. 6 in. x 30 ft. 5 in. 12. A man owns two fields of the following dimen- sions: 1$5 rd. 3% yd. wide and 225 rd. 2 yd. long; 464 rd. wide and 910 rd. 4 yd. long. How much fence will it. take for both fields? (49) 13. How many more rods of fence will be needed for a rectangle 580 rd. x 675 rd. than for a square field one side of which is 586 rd.? 14. How many rods of fence will be needed to enclose two fields, one 215 rd. 4 yd. long and 212 rd. 3 yd. wide; the other 80 rd. 4 yd, wide and 125 rd. 2 yd. long? 15. Find the perimeter of a trapezoid the length of its sides being 12 ft. 2 in., 15 ft. 1 in., 25 ft. 7 in., and 30 ft. 4 in. 16. How many posts set 8 ft. apart are required to enclose a field 160 rd. long and 96 rd. wide? 17. How many posts set one rd. apart will be needed for a triangular field whose sides are respectively 86 rd. 160 rd. and 126 rd. in length? 18. The perimeter of a square is 191 rd. 3 yd. 2 ft. Find the length of one side. 19. The perimeter of an equilateral triangle is 212 yd. Find the length of each side in feet. 20. A fence extends along both sides of a railroad 75 miles in length. Find the cost of the fence at 50c a rod. Exercise 25. To Supplement Page 225. When reducing square rods to acres carry the quo- tient out two decimal places. If quotient will come out even carry out three places. How many acres in a rectangular field: 1. 80 rd. wide and 120 rd. long? 2. 90 rd. wide and 125 rd, long? 3. 110 rd. wide and 230 rd. long? 4. 424 rd. wide and 575 rd. long? 5. 380 rd. wide and 462 rd. long? At $220 an acre find the cost of a rectangular tract of land: 6. 75 rd. wide and 120 rd. long. 7. 100 rd. wide and 165 rd. long. (50) 8. 226 rd. wide and 300 rd. long. 9. 55 rd. wide and 60 rd. long. 10. 28 rd. wide and 48 rd. long. Find in square yards the area of a rectangle: 11. 12 ft. wide and 25 ft. long. 12. 18 yd. wide and 34 yd. long. 13. 96 ft. wide and 104 ft. long. 14. 58 ft. wide and 74 ft. long. 15. 320 ft. wide and 427 ft. long. How many rods of fence will enclose a field con- taining : 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. inches. 32. 33. inches. 34. rods. 35. 55% acres and 210 rd. long? 80 acres and % mi. long? 99 9-16 acres and 88V 2 rd. wide? 44,460 sq. rd. and 228 rd. long? 233 acres 100 sq. rd., width 125 rd? 4 acres 44.7 sq. rd., and 33.4 i*d. long? 480 acres and % mi. wide? 642.5 acres and l^i mi. long? 5 acres and 50 rd. long? 1,885 acres, 75 sq. rd. and 475 rd. wide? How many square rods in 15 acres 43 sq. rd.? Change 1 sq. mi. to square feet. Reduce 120 acres 6 sq. ft. to square inches. In 83,635,200 sq. ft. how many square miles? A field 40 rd. square contains how many acres? Reduce 555 sq. yd. 5 sq. ft. 55 sq. in. to square Reduce 75 acres 75 sq. rd. to square rods. Reduce 30 sq. yd. 2 sq. ft. 36 sq. in. to square Reduce 5 sq. mi. 237 acres 135 sq. rd. to square Reduce 888 sq. yd. 8 sq. ft. 88 sq. in. to square 15 acres to square feet. (1 acre equals inches. 36. Reduce 43,560 sq. ft.) 37. Reduce 100,000 sq. rd. to acres. (51) 38. Reduce 37,625 sq. in. to higher denominations. 39. Reduce 1,040,100 sq. rd. to higher denominations. 40. Reduce 1,089,000 sq. ft. to acres. 41. Reduce 34,848,000 sq. ft. to higher denominations. 42. A parlor is 30 ft. long and 18 ft. wide. What is the area of its floor? 43. A garden is 20 rd. long and 6 rd. wide. How many acres does it contain? 44. A pasture is 45 rd. long and 32 rd. wide. What is its value at $75 per acre? 45. A room is 24 ft. long and 18 ft. wide. How many square yards of linoleum will cover it? 46. What will it cost to paint a ceiling 60 ft. long and 30 ft. wide at 15c a square yard? 47. How much did a real estate dealer receive for a farm 90 rd. long and 64 rd. wide, at $62.50 per acre? 48. A baseball park 750 ft. square is surrounded by a tight board fence 10 .ft. high. What is the fence worth at $3.25 per square? (A square is 100 St} ft.) 49. A rostrum 15 ft. long contains 10 sq. yd. of sur- face. How wide is it? 50. What must be the width of a twelve acre field if the length is 60 rd.? 51. At 15c each what will it cost to lay a floor 24 ft. long and 20 ft. wide with tiles 6 in. square? 52. A fair ground 80 rd. long was bought for $3,000 at $75 per acre. Find its width. 53. What will it cost to cement the floor of a cellar 36 ft. long and 24 ft. wide, at $1.25 per square yard. 54. How many pieces of sod 20 in. long and 9 in. wide will it take to cover a yard 36 ft.. long and 20 ft. wide? 55. What will it cost to lath and plaster a ceiling 36 ft. long and 24 ft. wide, at 24c a square yard? 56. How many tiles 15 in. square will be required to cover a floor 25 ft. long and 20 ft. wide? (52) 57. A field is 60 rd. wide. What must be the length to contain 30 acres? 58. The surface of a rectangular lot is 4680 sq. ft. At 2c a square foot what will it cost to build a close fence 5 ft. high around it, if the length of the lot is 72 ft.? 59. What will it cost to cement the bottom of a cellar 33 ft. long and 24 ft. wide, at $1.25 a square yard? 60. A tract of land cost $5,200 at $65 an acre. How long is it if its width is 64 rd? 61. How many tiles 10 in. wide and 16 in. long would cover the floor of a dining room 36 ft. 6 in. long and 26 ft. 8 in. wide? 62. A roof is 40 ft. long, and 15 ft. wide on each side. Find the cost of slating it at $7.50 per square. (A square equals 100 sq. ft.) 63. The slate blackboard in a school room is 33 ft. 4 in. long by 4 ft. 6 in. wide. What did it cost at 33V 3 c a square foot? 64. An enclosure is 55 rd. long, and contains 11 acres. What would be the cost of a tight board fence 5 ft. high surounding it, at $16 per thousand feet? 65. How much more fence would be required for a farm 108 rd. long and 75 rd. wide than for a square lot of equal area? 66. A square room contains 25 sq. yd. of carpet. If each side were 6 ft. longer, how many square yards would cover the floor? 67. The fence around a square pasture measures 192 rd. Find the area of the pasture in acres. PLASTERING. Exercise 26. Note To find the number of square feet in the walls of all rooms at once, multiply the perimeter of all the. (53) rooms by the height of the ceiling; to this result add the area of the .ceilings in square feet, after which reduce the total to square yards. Find the number of square yards of surface in the walls and ceiling of a room: 1. 18 ft. by 25 ft. ceiling 9 ft. high. 2. 26 ft. x 32 ft. ceiling 10 ft. high. 3. 55 ft. x 60 ft. ceiling 14 ft. high. 4. 110 ft. x 130 ft. ceiling 18 ft. high. 5. 15 ft. x 16 ft. ceiling 10 ft. 6 in. high. 6. At 40c per square yard find the cost of plastering four rooms, sizes as follows: 1'room 20 ft. x 26 ft. 6 in. ceiling 10 ft. 1 room 22 ft. 6 in. x 25 ft. 6 in. ceiling 10 ft. 1 room 32 ft. x 42 ft. ceiling 10 ft. 1 room 11 ft. x 12 ft. ceiling 10 ft. 7. Find the cost of plastering the rooms of a house at 40c a square yard. Deduct 10 sq. yd for openings. 1 room 11 ft. x 14 ft. ceiling 8 ft. 2 rooms 12 ft. x 14 ft. ceiling 8 ft. 1 room 14 ft. x 15 ft. ceiling 8 ft. 1 room 13 ft. x 15 ft. ceiling 8 ft. 1 hall 6 ft. 6 in. x 10 ft. ceiling 8 ft. Find the cost of plastering the walls and ceilings of rooms of the following dimensions at 30c per square yard, no allowance being made for openings. Consider any frac- tion of a square yard to be another square yard. Width Length Height 8. 18 ft. 20 ft. 10 ft. 9. 25 ft. 30 ft. 9 ft. 10. 21 ft. 25 ft. 9 ft. 11. 15 ft. 18 ft. 8 ft. 12. 12 ft. 15 ft. 8 ft. 13. 30 ft. 40 ft. 12 ft. 14. 20 ft. 21 ft. 9 ft. (54) Width Length Height 15. 18 ft. 30 ft. 8 ft. 16. 20 ft. 24 ft. 9 ft. 17. 18 ft. 6 in. 20 ft. 4 in. 10 ft. 18. 15 ft. 16 ft. 8 ft. 19. 15 ft. 6 in. 18 ft. 3 in. 9 ft. At 35 c. a square yard find the cost of plastering the five rooms of a dwelling: 20. 1 room 16 ft. 6 in. x 18 ft. ceiling 9 ft. 2 rooms 12 ft. x 15 ft. ceiling 9 ft. 1 room 10 ft. x 12 ft. ceiling 9 ft. 1 room 13 ft. x 15 ft. ceiling 9 ft. 21. How many square yards of plastering in the walls and ceiling of a room 16 ft. by 20 ft. and 9 ft. high, deducting 14 sq. yd. for the openings and baseboard? 22. How many square yards of plastering in the w^alls and ceiling of a hall 60 ft. long 40 ft. wide and 28 ft. high, deducting 36 sq. yd. for the openings and baseboard? 23. What will it cost to plaster a schoolroom 32 ft. long, 18 ft. \vide and 12 ft. high, at 32c a square yard, de- ducting 50 r ,'f of the area of the walls on account of black- boards, baseboards and openings? CARPETING. Exercise 27. To Supplement Page 225. 1. Find the cost of carpeting a room 18 ft. long and 15 ft. wide with carpet 1 yd. wide if the strips run length- wise. Price per yard 80c. 2. At $1.25 a yard find the cost of carpeting a room 12 ft. -x 15 ft. with carpet 27 in. wide if the strips run lengthwise. 3. At $1.10 a yard find the cost of carpeting a room 10 ft. x 12 ft. with carpet 2*4 ft. wide if the strips run cross- wise. (55) 4. At $1.50 per square yard find the cost of linoleum for a room 20 ft. by 25 ft. 5. Find the cost of linoleum for a hall 70 ft. x 90 ft. at $1.75 per square yard. 6. At 75c per yard find the cost of carpeting a room 15 ft. 6 in. x 16 ft. with carpet 1 yard wide if the strips run crosswise. 7. Carpet 27 in. wide is laid on a room 17 ft. x 18 ft. the strips running crosswise; 14 of a yard is allowed on each strip except the first for matching the pattern. Find the cost at $1.30 per yard. 8. At $1.75 per square yard find the cost of linoleum for a hall 75 ft. x 95 ft. 9. Allowing iy 2 ft. on each strip except the first for matching find the cost at $1.20 per yard of carpeting a room 14 ft. x 16 ft. with carpet 27 in. wide if the strips run lengthwise. 10. How many yards of carpet, 27 in. wide, will be required for a room 12 ft. 6 in. x 15 ft. 6 in. if the strips run crosswise and 2 ft. is allowed on each strip except the first for matching the pattern? 11. A sitting room, 16 ft. by 12 ft. is carpeted with ingrain carpet 1 yd. wide at 67c per yard. In order to match the figures, the carpet layer was obliged to cut off or .waste a piece of carpet % of a yard long from each strip except the first. How much did the carpet cost if the strips run lengthwise? 12. Allowing *4 of a yard to be turned in or cut off from each strip except the first in order to match the figures, how much will it cost to carpet a room 21 ft. x 18 ft. with carpet 27 in. wide, worth $1.35 per yard, t if the strips run lengthwise. 13. How many yards of carpet 27 in. wide will it take to carpet a room 16 y 2 ft. x 12 ft. if the strips run length- wise? What is the cost at 90c a yard? (56) 14. A man wishes to carpet a room 18 ft. x 16 ft. and does not wish to cut a strip or turn any carpet under. Which way must the strips run if the carpet is 27 in. wide? 15. Find the cost of carpeting a room, 14 1 /*, ft. x 13 ft. with carpet 1 yd. wide, worth 85c a yard, if the strips run lengthwise and % of a yard is allowed for matching on each strip except the first. 16. How many yards of carpet % of a yard wide will be needed to carpet a room 19 ft. x 14^ ft., if the strips run across the room? How many if the strips run length- wise? 17. Find the cost of linoleum, which is sold by the square yard for a floor 12% ft. x 11 ft. at 85c a square yard. LUMBER MEASURE AND SHINGLING. Exercise 28. To Supplement Pages 160-161; 225. If the thickness is less than one inch consider it one inch. How many feet board measure? 1. In 12 planks 3 in. thick, 12 ft. long, 12 in. wide? 2. In 18 planks 4 in. thick, 16 ft. long, 10 in. wide? 3. 'In 14 planks 2 in. thick, 18 ft. long, 10 in. wide? 4. In 2 sticks of timber 18 ft. long, and 1 ft. square? 5. In -30 joists 10 in. by 2 in. and 18 ft. long. 6. In 40 joists 8 in. by 2 in. and 16 ft. long? 7. In 60 joists 3 in. x 4 in. and 12 ft. long? 8. In 4 beams 14 in. by 12 in. and 30 ft. long? 9. In 40 boards % in. thick, 8 in. wide and 14 ft. long? 10. In 50 inch-boards that are 5 in. wide and 16 ft. long? 11. In 100 planks 2 in. thick, 12 in. wide and 18 ft. long? 12. In 24 sticks 7 in. by 8 in. and 20 ft. long? 13. In 20 beams 10 in. by 12 in. and 30 ft. long? (57) 14. In 36 joists 3 in. by 9 in. and 16 ft. long? 15. How many feet of lumber in a floor 15 ft. long, 12 ft. wide and 1 in. thick? 16. A bridge 84 ft. long and 20 ft. wide is covered with oak plank 2V 2 in. thick. What is it worth at $16 per M.? 17. How much lumber 1 in. thick will be required to cover a walk 5 ft. wide around a rectangular lawn 300 yd. long and 200 yd. wide? 18. What is the number of board feet in a stick of timber 30 ft. long and 18 in. square? 19. A- two-inch plank, 9 in. wide at one end and 15 in. wide at the other, tapers gradually; how much lum- ber is there in it, the length being 18 ft.? 2.0. At $20 per thousand, find the whole cost of 5 scantling 20 ft. long, 4 in. wide, 3 in. thick; 9 scantling 18 ft. long, 5 in. wide, 4 in. thick; 6 scantling 14 ft. long, 6 in. wide and 5 in. thick. 21. Find the cost of the following bill of lumber: 10 pc. 2 in. x 4 in. x 14 ft.; 12 pc. 2 in. x 6 in. x 16 ft.; 20 pc. 2 in. x 8 in. x 18 ft.; 24 pc. 4 in. x 4 in. x 20 ft.; 20 pc. 4 in. x 8 in x 20 ft., at $21 per M.; 96 pc. 2 in. x 12 in. x 16 ft.; 75 pc. 2 in. x 10 in. x 18 ft. at $25 per M. 22. At $30 per M what will the lumber cost for siding a house 30 ft. long, 24 ft. wide and 16 ft. high, 30 sq. yd. being allowed for doors and windows ajid the gable ends being counted 544 sq. ft. 24. Allowing 1000 shingles for 100 sq. ft. how many thousand will be required to cover the pitched roof of a house 36 ft. long, if the width of each side of the roof is 21 ft.? 24. Allowing 1,000 shingles for 100 sq. ft. how many thousand would be required to cover four walls of a flat-roofed house 42 x 36 ft. and 22 ft. high, allowing 500 sq. ft. for doors and windows? (58) 25. How many slates at 3 to the square foot will be required to cover 13 squares of roof? 26. Find the cost of a floor for a room 18 ft. x 16 ft., at $22 per square. 27. Find the cost of a birch floor for a room 16 ft. x 15 ft. if birch floor-boards are worth $40 a thousand feet, and if the waste is reckoned at y 5 of the area of the floor. 28. Find the cost of laying an oak floor for a dining room 16 ft. x 17 ft., reckoning the nails and labor at $12, the oak floor boards at $80" a thousand, and the waste at 34 sq. ft. AREA OF TRIANGLES. Exercise 29. To Supplement Page 226. Find the area of triangles having: 1. Base 90 ft. and altitude 82 ft. 2. Base 125 ft. and altitude 95 ft. 3. Base 114 ft. and altitude 59 ft. 4. Base 160 ft. and altitude 100 ft. 5. Base 225 ft. and altitude 160 ft. 6. Base 240 ft. and altitude 180 ft. 7. Base 260 ft. and altitude 200 ft. S. Base 400 ft. and altitude 345 ft. 9. Base 550 ft. and altitude 475 ft. 10. Base 600 ft and altitude 800 ft. 11. Base 750 ft. and altitude 950 ft. 12. How many acres are there in a rectangular* field 145 rd. long and 86 rd. wide? 13. A rectangular field contains 2% acres and is 12 2-9 rd. wide. How many rods long is the field? 14. A city lot in the shape of a triangle has a base of 82 ft. and an altitude of 45 V 2 ft. What is the value of th lot at $5.50 a square foot? -(59) 15. How many paving blocks 8 in. x 2 in. will be needed to pave a street 250 ft. long and 40 ft. wide, making no allowance for spaces between the blocks? 16. What is the cost of concreting a walk 82*4 ft. x 6 ft. at 70c a square yard? 17. A rectangle and a triangle have equal areas. The rectangle is 18 1-6 ft. x 14 ft.; the altitude of the triangle is 22 ft. What is the base of the triangle? 18. What is the area of an equilateral triangle whose perimeter is 37 ft. 6 in. and whose altitude is 10.82 ft.? 19. What is the base of a triangle whose altitude is 6.4 rd. and area y 2 - acre? Altitude 7.2 in. and area V 2 sq. ft.? 20. A right angled triangle has two sides forming the right angle 30 rd. and 40 rd. What is its area in square rods? In acres? 21. What is the number of square feet of slating re- quired for a steeple, the surface being made up of 6 triangles each with a base 20 ft. and altitude 65 ft.? AREA OF PARALLELOGRAMS; TRAPEZOIDS. Exercise 30. To Supplement Pages 227-230. 1. Find the area of a rhomboid whose longer sides are 9 in. apart, and are each 48 in. long. Supply the missing numbers in the measurements of the following rhomboids: Base Altitude Area 2. 40 in. 5 in. x sq. in. 3. x in. 10 in. 60 sq. in. 4. 25 in. x in. 175 sq. in. 5. 13.8 in. x in. 55.2 sq. in. 6. x in. 2,5 x /2 in. 10.2 sq. in. 7. 5 ft. x in. 2 sq. ft, 12 sq. in. (60). 8. The perimeter of a certain rhomboid is 60 in. The base is 20 in. The altitude is 6 in. Represent and find the area. 9. A base of a rhomboid is 5 in. longer than the altitude which is 16 in. What is the area of the rhom- boid? Find the area of trapezoids of the following dimen- sions: 10. Parallel sides 56 and 108 ft., altitude 40 ft. 11. Parallel sides 60 and 118 ft., altitude 45 ft. 12. Parallel sides 64 and 126 ft., altitude 25 ft. 13. Parallel sides 68 and 110 ft., altitude 35 ft. 14. Parallel sides 70 and 112 ft., altitude 45 ft. 15. Parallel sides 72- and 138 ft., altitude 42 ft. 16. Parallel sides 76 and 144 ft., altitude 44 ft. 17. Parallel sides 80 and 150 ft., altitude 60 ft. 18. Parallel sides 84 and 162 ft., altitude 37 ft. 19. Parallel sides 88 ft. and 170 ft., altitude 26 ft. Find the area of the trapezoids as follows: Altitude Parallel Sides 20. 5 rd. 6 rd. 7 ft. and 9 rd. 21. 322 ft. 427 ft. and 534 ft. 22. 127 ft. 120 ft. and 148 ft. 23. 236 in. 208 in. and 235 in. 24. 34 ft. 27 ft. 8 in. and 33 ft. 25. 62 ft. 3 in. 59 ft. and 78 ft. 26. 4 yd. 2 yd. 27 in. and 6 yd. CIBCLES. Exercise 31. To Supplement Pages 231-232. (Use 3 1-7) Find the circumference and area of a circle whose 1. Radius is 42 ft. 2. Radius is 56 ft. (61) 3. Radius is 27 ft. 4. Radius is 28 in. 5. Radius is 32 rd. 6. Diameter is 20 ft. 7. Diameter is 36 yd. 8. Diameter is 25 ft. 6 in. Find the radius and area of a circle whose 9. Circumference is 52% ft. 10. Circumference is 176 ft. 11. Circumference is 75 3-7 ft. 12. Circumference is 55 ft. 13. Circumference is 40 6-7 ft. 14. Circumference is 44 ft. 15. Circumference is 616 rd. 16. What is the area of a circle whose diameter is 36 ft.? 17. A circular park requires 176 rd. of fence to en- close it. How many acres does it contain? 18. Find the area of a space on which a horse may graze when confined by a rope 105 ft. long. 19. A circular fish pond has a radius of 75 ft.; w r hat is its area? 20. How many square yards in a circular grass plot 72 ft. in diameter? 21. The diameter of a circular race course is 750 yd. Find the circumference. 22. What is the diameter of a water tank whose cir- cumference is 74.8 ft.? 23. What is the circumference of a rod whose dia- meter as measured by calipers is 2.1 in.? 24. What radius must be used in drawing a pattern for a wheel that shall be 88 in. in circumference? 25. How much fence will be required to inclose a circular field 25 rd. in diameter? (62) 26. A cow is tied to a stake by a rope 26 ft. long. Over what area can she graze? 27. At $140 an acre, what is the value of a circular tract of land 200 rd. in diameter? 28. What is the area of a circular park whose cir- cumference is a race track one mile in length? 29. A circle 40 ft. in diameter has within it another circle 30 ft. in diameter. What is the area of the ring between the two circumferences? KEYIEW. Exercise 32. To Supplement Pages 221-232. 1. Reduce 5 mi. 5 yd. 2 ft. to feet. 2. Reduce to higher denominations 43,735 ft. 3. Reduce 67,314 sq. yd. to higher denominations. 4. Find % of 5 mi. 80 rd. 3 yd. 1 ft. 5. A farm is rectangular in form, 75 rd. wide and 96 rd. long. What is it worth at $66 an acre? 6. A field is 45 rd. wide and' contains 36 acres. How long is it? 7. A pasture is 48 rd. wide, and contains 15 acres, How long is it and what would be the cost of a fence around it at 95c a rod? 8. A meadow is 68 rd. long and its area is 23 acres 60 sq. rd. What would be the cost of the fence suround- ing it, at 85c a rod? 9. A lot is 66 feet wide and its area is 10,890 sq. ft. A close board fence five feet high surrounds it. Find its value, at l^c a square foot. 10. How many sheets of paper 9 in. long and 6 in. wide can be cut fom a roll 2 yd. wide and 50 yd. long? 11. A cellar is 33 ft. long and 21 ft. wide. Find the cost of cementing the floor, at $1.30 a square yard. (63) 12. A city lot is bounded by four streets, two of which are parallel and extend along the side of the lot 90 ft. and 110 ft. If the two streets are 80 ft. apart, what is the area of the lot? 13. The fence around a square field is 120 rd. long. How many acres does the field contain? 14. At 25c a square foot what will be the cost of a blackboard 36 ft. 8 in. long and 4 ft. 6 in. wide? 15. What is the rent of a triangular field whose base Is 80 rd. and perpendicular height 48 rd. at $4.50 per acre? 16. At $60 per acre a farm in the form of a trapezoid sold for $2,700. If the width is 40 rd., and one of the parallel sides is 259c longer than the other, what are their respective lengths? 17. The gable end of a house was 34 ft. 6 in. from eave to eave and the perpendicular height of the ridge above the eaves is 13 ft. How many feet of boards will be required to cover three such gables? 18. How many small squares each containing 4 sq. in. are contained in a large one which is 4 ft. square. 19. What will it cost to plaster a room 15 ft. 6 in. long, 12 ft. 9 in. wide and 10 ft. 3 in. high at 37 %c per square yard? 20. How many yards of carpeting % yd. wide will cover a floor 16 ft. 9 in. long by 15 ft. 9 in. wide, if laid lengthwise. 21. A lot of ground 80 ft. long by 20 ft. wide was cut diagonally by a railroad, leaving a triangular plot of the same base and altitude. What was its area? How many feet, board measure, in the following: 22. 16 joists 2 in. by 4 in. and 13 ft. long? 23. 40 two-inch planks, 14 in. wide and 14 ft. long? 24. 36 three-inch planks, 9 in. wide and 20 ft. long? 25. A stick 1 ft. by 1 1-6 ft. and 27 ft. long? 26. ' What will it cost at $1.60 per hundred to build a sidewalk 40 yd. long, 6 ft. wide, with planks % in. thick? (64) 27. What will it cost to plaster the sides and ceiling of a room 36 ft. 9 in. long, 27 ft. 6 in. wide and 10 ft. 6 in. high, at 21c per square yard, if 28 sq. yd. are allowed for doors and windows? 28. Find the cost of carpeting a room 36 ft. long, 28 ft. wide with carpet % yd. wide, laid lengthwise, at $1.15 per yard? 29. Find the number of strips of carpet 1% yd. wide run lengthwise of a floor 32 ft. long and 27 ft. wide. What does it cost at $1.10 per yard, allowing a waste of *4 of a yard on each strip for matching except the first? 30. How many boards 15 ft. long will be required to build a straight fence 4 boards high about a rectangular field 60 rd. long and 30 rd. wide? 31. A rectangular lot 150 ft. deep fronts on a certain street. The lot contains an acre, and is sold for $20 a front foot. How much is received for the lot? 32. A man paid $7,888.30 for 89 acres 90 sq. rd. of land. What was the price per acre? 33. How many yards of carpet 27 in. wide will be needed for a room 18 ft. long and 17 ft. 6 in. wide, if the strips run lengthwise, and if there is a waste of 9 in. on each strip except the first in matching pattern? 34. Find the cost at 15c a square yard of painting the outside of the walls of a cottage roofed house 36x32x13 ft. 35. Find the cost at 15c a square yard of painting the outside walls of a house 42 ft. x 32 ft. x 19 ft. with gables extending 10 ft. above the end walls, the two gables to be reckoned as one full wall 32 ft. x 10 ft. 36. A field in the shape of a trapezoid measures 67 rd. and 53 rd. along its parallel sides and is 75 rd. long. What is its value at $80 per acre? 37. A field in the form of a trapezoid is 60 rd. long and its area is 16 acres and 20 sq, rd. If one of the parallel sides is 48 rd. long, what is the length of the other? (65) 38. What is the cost of the material for fencing a field % of a mile wide and % of a mile long, posts set a rod apart at 23c each; 26 in. hog wire fencing at the bottom costing $2.60 per hundred lineal feet, with two strands of barbed wire above costing 30c per hundred lineal feet, allowing 160 Ib. of nails and staples at 4 1 /c per pound? 39. A man buys 800 apple boxes 9 in. x 11 in. x 20 in., the ends made of one-inch material and the top, bottom and sides of ^-inch material. What will the material cost at $28 per thousand? 40. Mr. Pomroy built a basement 10 ft. 6 in. x 16 ft. The city ordinance required that for each 10 sq. ft. floor space or major fraction thereof there should be at least one sq. ft. of window glass surface. How many square feet of glass would be required? 41. At $24 per thousand feet what would be the cost of building a bridge requiring the following list: $3 is al- lowed for nails and $58 for labor? 4 pieces 6 in. x 12 in. x 24 ft. for stringers. 3 pieces 8 in. x 12 in x 16 ft. for caps. 12 pieces 8 in. x 8 in. x 6 ft. for posts. 6 pieces 2 in. x 6 in. x 16 ft. for braces. 24 pieces 3 in. x 12 in. x 16 ft. for covering. 42. What will be the cost of a car load of lumber itemized as follows: 168 pieces 1 in. x 12 in. x 16 ft. 33 pieces 1 in. x 8 in. x 14 ft. 124 pieces 2 in. x 10 in. x 26 ft. 40 pieces 6 in x 6 in. x 18 ft. 1280 lineal ft. 2 in. x 4 in. The above to cost $22 per thousand. 1400 sq. ft. 1 in. x 4 in. tongue and grooved flooring at $47 per thousand. 4,800 sq. ft. 1 in. x 12 in. ship lap at $26.50 per thous- and. 43. At $21.50 per thousand board feet what will be the cost of the ties required to build 5.4 miles of railroad if the ties are 6 in. x 8 in. x 8 ft. and are placed 22 inches