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More Exercises for the Slate

1. If 25 men, by working 10 hours a day, can dig a trench 33 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?

this example, the second terms, 25 x 48 x 8 x 5 x 9,= 432000, Che first terms, 15 x 36 x 12 x 6 x 12, 466560. Then, the third terra 40X432000,=43200004665609 h. 158 m., the fourth term, or Ans,

Or, by multiplying the third term by the ratios, thus: the ratio of 15 to 25 is, of 36 to 48 is, of 12 to 8 is, of 6 to 5 is, of 12 to 9 is, whose products, multiplied by the 5X4X2X5 x 3 x 10 h. X3X3X6X4

third term, are

Ans., as before.

6000
648

h. 9 h. 153 m

This method, it will be perceived, is much shorter than the former. Bu 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 4X2X5 x 3 x 10 h. 3X3X3X6X4

in T XLI; thus, the ratios.

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5x2x5x 10b 3X3X6

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 5 201
Days 6 18

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In this example, the ratios of 5 to 20, and of 6 to 18, are 3 and then, 3 x 4 x 10 rods: = 1:20 rods, Ans.

The same by analysis. I man will build of 10 rods, -, in 6 days, and in 1 day of 10-48; that is, 1 man will build of 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.

5 If 8 men, 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 inay 4 men be hired for $24? A. 6 days.

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7. If 9 persons in a family spend $1512 in 1 year (or 12 mno.), 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 x 3 mo. = =2.) A. 21 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? A. 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 and, 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 $1) a yard, what will 4 yds. cost? What will 12 yds.? What will 40 yds.? What will 300 yds.?

3. At $,331 (or $3), what will 6 yds. cost? What will 9 yds.? Will 24 yds.? Will 300 yds.? Will 7 yds.? Will 25 yds.?

4. At $,163 (or $), 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 $,121 (or $) a yard, what will 16 yds. cost? Will 06 yds.? Will 97 yds.? Will 100 yds.?

6. At $,061 (or $T), what will 33 yds. cost? Will 66 rds.?

7. What will 4 qts. of molasses cost, at 2 cents a gill? 8. How many shillings in 4£.? In 8£.? In 3. 5a) How many minutes in 8 hours? In 12 hours?

how

10. How many cents is 16 $t? Is $? Is $4?

$? Is $? Is $1? 818?

of a dollar? Is $? Is $t? Is $? Is $3? Is $76? Is

Is $? Is $? Is $? Is

11. How many pence in 3 s. 9 d.? In 8s. 6d. ?

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 s. 3 d.?
15. What kind of a fraction is ? Is 14? Is

25? Is ?

16. What mixed number is equal to ? ?

17. How many 5ths in 8? In 4?

18. How many pounds in 8£.? In 98£?

of? Is

19. How many pounds and shillings in 10%£.? (£. is 18.) In 85.?

20. How many shillings in 3 d.? In 144 d.?

21. What fraction is equal to ???
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 ? ? ? 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? s.? (ts. is of 12 d. 2 d.) shilling?

27. How much is of? Is of ? Is of 1? 28. How much is 3 times ? 3 times ? 3 times 77 29. A man bought of a barrel of flour for 3 dollars; how much was it a barrel ?

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37. 3 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?

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43. William gave away 1 apple and §, which was § of all he had; how many had he? is 3 times as much as; hence, if 14 is of a certain number, the number must be 3 times 1; thus 14=2; then ×3=2=4}, Ans.

44. 2 is of what number? (If 24 is,, or the num ber, is 5 times as much; that is, 5 times 2) 114, Ans. 45. 1 is of what number?

46. 1 is 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. 49. Divide 3,5 by ,07. 50. Multiply 5 by 7. 51. Multiply 50 by,07. 52. How much will bushel?

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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 62 Of 6 to 9? Of 10 to 100?

61. If 20 bushels of apples cost $10, what will 5 buskels 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 & 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 per cent.? 20 per cent.?

77. William bought a sled for $3, and sold it so as to gain 10 per cent.; what did he get for it?

Exercises for the Slate.

1. Bought 1 gallon of molasses for 62 cents, 1 quarter of flour for $1,124, 3 lbs. of tea for $1,05, 3 yards of flannel for ,874, and 1 skein of silk for 64 cents; what was the amount of the whole? A. $3,733.

2. Bought 144 lbs. of raisins for $16; what was that a pound." 4. $,111+.

3. What is the cost of 3600 yards of flannel at $,12} a yard ?❤ 450. At $,334-1200. At $,20?-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 $84, sold 1 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 gr. 15 lbs.,

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