15 men : More Exercises for the Slate. 1. If 25 men, by working 10 hours a day, can dig a trench 36 feet long, 12 feet broad, and 6 feet deep, in 9 days, how many hours a day must 15 men work, in order to dig a trench 48 feet long, 8 feet broad, and 5 feet deep, in 12 days? : 25 men :: 48 length 6 depth 5 depth 12 days 9 days In this example, the second terms, 25 X 48 X 8 X 5 X 9,= 132000, and the first terms, 15 X 36 X 12 X 6 X 12,= 460560. Then, the third term, 10 X 432000,=4320000 --- 466500 = 9 h. 159 m., the fourth term, or Ans. Or, by multiplying the third term by the ratios, thus : the ratio of 15 to 25 is = 3, of 36 to 48 is 5, of 12 to 8 is, of 6 to 5 is /, of 12 to 9 is ^, whose products, multiplied by the 5 X 4 X2 X 5 X 3 X 10 h. 6000 third term, are h. -9 h.153 m., X3 X 3 X 6 X 648 Ans., as before. This method, it will be perceived, is much shorter than the former. But, had we selected terms whose ratios would be whole numbers, the process would have been shorter still, as is the case in the next question. The present example, however, may be rendered more simple by rejecting equal terms, as 5 X 4 X2 X5 X3 X 10 h. 5 X 2 X 5 X 10 h. in 1 XLI.; thus, the ratios 3 X 3 X 3 X 6X4 3X3X 6 500 9 h. 157 m., Ans., as before. 54 Let the pupil perform the following examples by the common rule of proportion first, then by multiplying by the ratio, and lastly by analysis. 2. If 5 men can build 10 rods of wall in 6 days, how many rods can 20 men build in 18 days? Men 5 : 20 ? : : 10 rods : rods. In this example, the ratios of 5 tn 20, and of 6 to 18, are 3 and 4; then, 3 X 4 X 10 rods=120 rods, Ans. The same by analysis. 1 man will build ; of 10 rods, = in 6 days, and in 1 day of 30=}; that is, 1 man will build šof a rod a day; then, 20 men X 18 days X ! 120 rods, Ans., as before. 3. If 4 men receive $24 for 6 days' work, how much will 8 men receive for 12 days' work? A. $96. 4. If 4 men receive $24 for 6 days' work, how many men may be hired 12 days for $96 ? A. 8 men. 10 5. If 8 inen, in 12 days, receive $96, how much will 4 men receive for 6 days' work? A. $24. 6. If 8 men receive $96 for 12 days' work, how long may 4 men be hired for $24? A. 6 days. 7. If 9 persons in a family spend $1512 in 1 year (or 12 mo.), how much will 3 of the same persons spend in 4 months ? A. $168. 8. If $2000 will support a garrison of 150 men 3 months, how long will $6000 support 4 times as many men? (The ratios are 3 and ; then, 3 x 4 x 3 mo.=1.) 4.24 mo. 9. If $100 gain $6 in 1 year, what will $900 gain in 8 months : A. $36. 10. If $100 gain $6 in 1 year, in what time will $900 gain $36? 11 8 months." 11. If the transportation of 12 cwt. 3 qrs., for 400 miles, cost $57,12, what will the transportation of 10 tons, for 75 miles, amount to? A. $168. 12. An usurer put out $150 at interest, and when it had been on interest 8 months, he received for principal and interest, $160, at what rate per cent. per annum did he receive interest ? By cancelling the ratios 3 and f, the third term will be the answer, A. 10 per cent. Questions on the foregoing. 1. What will 2 yds. of cloth cost, at 50 cents (or $1) a yard? What will 10 yds.? What will 100 yds.? What will 5 yds.? What will 9 yds.? 2. At 25 cents (or $4) a yard, what will 4 yds. cost? What will 12 yds.? What will 40 yds.? What will 300 yds. ? 3. At $,33} (or $!), what will 6 yds. cost? What will 9 yds.? Will 24 yds. ? Will 300 yds.? Will 7 yds.? Will 25 yds.? 4. At $,16(or $1), what will 12 yds, cost? Will 13 yds. cost? Will 14 yds. cost ? Will 25 yds. cost? Will 120 yds.? Will 300 yds.? 5. At $,12} (or $}) a yard, what will 16 yds. cost? Will 96 yds.? Will 97 yds.? Will 100 yds.? 6. At $,061 (or $16), what will 33 yds. cost? Will 66 yds.? 7. What will 4 qts. of molasses cost, at 2 cents a gill? 8. How many shillings in 4£.? In 8£.? In 3£. 5 s.? 9. How many minutes in 8 hours ? In 12 hours ? 10. How many cents is f of a dollar? Is $16? Is $t? Is $1? Is $}? Is $1? Is $36? Is $? Is $16? Is $16? Is $3? Is $11? Is $? Is $18? Is $3? Is $16? 11. How many pence in 3 s. 9 d.? In 8 s. 6 d.? 12. How many cents in 2 s.? In 3 s.? In 3 s. 9 d.? 13. How many cents will buy 3 slates, at 1 s. 9 d. each? 14. How many cents are 18 d.? Are 2 s.6 d. ? Are 5 8.3 d. ? 15. What kind of a fraction is f? Is 143 ? Is i of ? Is 3? Is ? 16. What mixed number is equal to 10? 17? 19. How many pounds and shillings in 1026£.? (28£. is 1 s.) In 8. $£.? 20. How many shillings in 36 d. ? In 444 d.? 21. What fraction is equal to $? 1.? ? 22. What kind of a fraction is ,5 ? Is 14,3 ? 23. What will be the cost of 3 books, at $,5 apiece ? At $,25 ? 24. What decimal fraction is equal to 1? ? 25. Bought ,4 of a bushel of rye at one time; at another, 25; and at another, ,35; how much did I buy in all ? 26. How much is of a shilling? és.? (fs. is $ of 12 d.= 2 d.) shilling? 27. How much is of 1? Is it of $? Is of 1? 28. How much is 3 times ]? 3 times f ? 3 times 3 ? 29. A man bought of a barrel of flour for 3 dollars; how much was it à barrel? 30. 3 is of what number? 31. 5 is of what number? 32. 10 is of what number? 33. 7 is f of what number? 34. of is of what number? 35. of 12 is of what number? 36. of 12 is of what number? 37. of 12 is of what number? 38. If a man save $ of a dollar a day, how many dollars will he save in 16 days? How many in 17 days? In 25 days? ? 39. In Lo how many times 1? 40. In 17 how many times 1 ? 41. In 4 how many times 1? 42. In 144 how many times 1 ? 43. William gave away 1 apple and d, which was $ of all he had ; how many had he? f is 3 times as much as }; hence, if it is } of a certain number, the number must be 3 times 14; thus 13 = 3; then * X3=3=43, Ans. 44. 21. is } of what number? (If 21 is }, }, or the number, is 5 times as much; that is, 5 times 2 =) 114, Ans. 45. 18 is of what number? 46. 1ş is 7 of what number? 47. William gave $,25 for 2,4 yds. of ribbon; how much was it a yard ? 48. Divide 3,5 by ,7. A. 5. 49. Divide 3,5 by ,07. A. 50. 50. Multiply 5 by ,7. A. 3,5. 51. Multiply 50 by ,07. A. 3,5. 52. How much will } of a peck of salt cost, at $1 & bushel ? 53. How many drams is $ of an ounce ? 57. If you pay 6 cents a quart for ale, how much is that a gallon? 58. If a man earn $3 a week, how much is that for each working day in a week? 59. If a man travel 6 miles in 2 hours, how far will he travel in 16 hours? 60. What is the ratio of 2 to 6? Of 6 to 2? Of 9 to 6? Of 6 to 9? Of 10 to 100 ? B. 61. If 20 bushels of apples cost $10, what will 5 bushels cost? 62. What is the ratio of 20 to 5? 63. If 6 gallons of water fall into a cistern, containing 12 gallons, in 1 hour, and 3 gallons leak out in an hour, how long will it take the cistern to be filled ? 64. If 4 men, in one day, consume 3 loaves of bread, how many loaves will 12 men consume in 4 days? 65. If 6 men, in 12 days, reap 18 acres of grain, how, many acres will 12 men reap in 4 days? 66. What part of 1 month is 15 days? Is 1 day? Is 2 days ? Is 3 days? Is 5 days ? . Is 10 days ? Is 20 days? 67. What is the interest of $20 for 4 months ? For 10 months ? For 3 months ? For 1 year 4 months ? 68. What is the amount of $40 for 2 mo.? For 5 mo.? For 10 mo.? For 1 yr. 8 mo.? 69. What is the interest of $60 for 15 days ? For 10 days? For 1 day? For '5 days ? For 2 mo. 15 days ? For 4 mo. 10 days? For 1 yr. 8 mo. 15 days? 70. What must you pay a broker, who gives you $20 in Boston bills, in exchange for Providence bills, at per cent. commission ? At 4 per cent.? At 1 per cent. ? 71. What is my demand for selling $600 worth of cotton, and guarantying the payment, at 5 per cent. commission ? At 7 per cent. commission? At 4 per cent. ? 72. What is the amount of $1 for 1 yr. 8. mo. ? 73. What is the amount of $200 for 1 yr. 8 mo.? 74. What, then, is the present worth of $220, due 1 yr. 8 mo. hence ? 75. What is the present worth of $530, due 1 yr. hence? What is the discount ? 76. A merchant, having bought cloth for 50 cents a yard, wishes to mark it so as to gain 10 per cent.; what price must he put on it ? (,50 x 110 = $,55, Ans.) What price must he put on it to gain 4 per cent. ? 8 cent. ? 20 per cent. ? 77. William bought a sled for $3, and sold it so'as to gain per cent.; what did he get for it? 10 Exercises for the Slate. 1. Bought 1 gallon of molasses for 62} cents, 1 quarter of flour for $1,121, 3 lbs. of tea for $1,05, 3 yards of flannel for $,87), and í skein of silk för 61 cents; what was the amount of the whole ? A. $3,73 2. Bought 144 lbs. of raisins for $16'; what was that a pound? A. $,111 +: 3. What is the cost of 3600'yards of flannel, at $,12}a yard?450. At $,333 ?-1200. At $,207-720. A. $2370. 4. In 20 lbs. of silver, how many spoons, each weighing 5 oz. 10 pwt.? A. 43 spoons, and 3 oz. 10 pwt. rem. 5. A bought 4 hogsheads of molasses for $34, sold' l'hogshead for $25, and the remainder at the rate of 4 cents a' pint; how much did he make on the whole ? A. $1,48. 6. Bought a hogshead of sugar, weighing 12 cwt. 1 qr. 15 lbs., |