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of the week, can in 4 weeks dig a trench 450 feet long, 34 feet wide, and 2 feet deep, how many men, working 9 hours per day during 5 days of the week, can in 9 weeks dig a trench 539 feet long, 64 feet wide, and 211 feet deep?

28. If 12 men, by working 94 hours per day during 5 days of the week, can in 9 weeks dig a trench 539 feet long, Of feet wide, and 211 feet deep, how many weeks would it take 9 men, working 10 hours per day during 6 days of the week, to dig a trench 450 feet long, 31 feet wide, and 2 feet deep?

29. If 36 lb. of sugar are worth 24 lb. of coffee, and 22 Ib. of coffee are worth 55 lb. of rice, how many pounds of rice can be bought for 16 lb. of sugar ?

Preliminary Explanation. As the answer is to be pounds of rice, we must write 55, the given number of pounds of rice, as the number to be operated on, and must take care to express the values throughout in pounds of rice. We should then have the following

Solution. Since 22 lb. of coffee are worth 55 lb. of rice, 1 lb. of coffee must be worth of 55 lb. of rice, which may be expressed by writing 22 as a denominator under the 55; and 24 lb. of coffee must be worth 24 times the last result, which may be expressed by making 24 a factor of the numerator. But as this is also the value of 36 lb. of sugar, 1 lb. of sugar must be worth 36 of this, which may be expressed by making 36 a factor of the denominator; and 16 lb. of sugar must be worth 16 times the last result, which may be expressed by making 16 a factor of the numerator. The work would be written thus:

5 12

55 X 24 X 16 lb. of rice

263 lb. of rice = Ans. 22 X 36

2 3 Note. -- Examples like the above are usually solved by a process called ConjoinED PROPORTION; but as it is much less simple and con venient than the preceding, we omit it.

30. If 40 bushels of potatoes are worth 45 bushels of corn, and 18 bushels of corn are worth 14 cwt. of hay, and 35 cwt. of hay are worth 4 barrels of flour, how many barrels of Aour are 75 bushels of potatoes worth ?

31. If 7 American yards are equal to 12 braces at Lego horn, and 54 braces at Leghorn are equal to 45 braces at Venice, how many braces at Venice are equal to 56 American yards?

32. If John can earn as much in 7 days as William can earn in 9 days, and William can earn as much in 15 days as Samuel can in 14, and Samuel can earn as much in 12 days as Otis can in 8, and Otis can earn as much in 24 days as Rufus can in 21, how many days will it take John to earn as much as Rufus can earn in 49 days?

33. Multiply 521 by 7}, subtract 14 from the product, and divide by }

34. A man gave 41 acres of land, worth $125.37 per acre, in exchange for 75 barrels of four. He sold s of the flour at $93 per barrel, and the rest at $8! per barrel. How much did he gain by the transaction ?

35. A garrison of 2000 men had bread enough to allow each 24 oz. a day for 75 days; but being besieged, it received a reënforcement of 1600 men. How many ounces per day can each man be allowed, in order that they may hold out 60

days?

36. Half of Arthur's money equals just z of William's, and William has $187.47 more than Arthur. How much money has each ?

155. Practice. The following examples illustrate what is sometimes called the Rule OF PRACTICE.

1. How much will 47 yd. 3 qr. 3 n. of broadcloth cost, at $3.125 per yd.?

Suggestion. — Since 47 yd. 3 qr. 3 na. lacks but I nail of being 49 •rds, its cost must equal the cost of 48 yards, minus the cost of Ir il

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48 X a=

b $150.000 = cost of 48 yds. It of a=c=$ .195 =

1 na. b-C= $149.805 “ 47 yds. 3 qr. 3 na.

2. How much will 26 A. 1 R. 25 sq. rd. of land cost, at $174.25 per acre ?

WRITTEN WORK.

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[ocr errors]

= e =

26 X a=b= $4530.50 =

« 26 A.
of a=c= 43.562

R.
of c= :d 21.781 = “ 20 sq. rd.
of d

5.445

“ 5 sq. rd. b+c+d te=

e= $4601.288 = " 26 A. i R. 25 sq. rd. Note. — In dividing, in examples like the above, it is unnecessary to carry out the work further than to mills.

3. How much will 13 lb. 4 oz. 10 dwt. 8 gr. of silver cost at $13.37 per lb. ?

4. How much will 9 T. 15 cwt. 1 qr. 14 lb. of English bar iron cost, at $83.625 per ton, reckoning the quarte 28 lbs.? (See 34, c.)

5. How much will it cost to build a road 37 m. 5 fur. 30 rd. in length, at the rate of $2173.75 per mile ?

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+ 38 m. 66 2 fur. 6 10 rd.

38 X a=b= $82602.50

of a=c=$ 543.437 = f of c= d=$ 67.929

b d=$81991.134 = cost of 37 m. 5 fur. 30 rd. 6. How much will 22 hhd. 21 gal. 3 qt. 1 pt. of wine cost, at $47.875 per hhd., if each hogshead contains 63 gallons ?

7. How much will 24 bu. 1 pk. 6 qt. of wheat cost, at $1.375 per bushel ?

8. How much will 37 bu. 3 pk. 4 qt. of wheat cost at $1.625 per bushel ?

9. How much will 14 cwt. 2 qr. 15 lb. of coffee cost, at $12.625 per cwt. ?

10. A man' bought a farm, containing 137 A. 3 R. 30 sq. rd., at $46.94 per acre ? How much did it cost him ?

11. A trader bought 184 bu. 2 pk. 6 qt. of Indian corn, at $ 875 bushel. How much did it cost him ?

per

12. How many rods will a man travel in 13 h. 20 m. 45 sec., if he travels 1289 rods

per

hour? 13. What will 24 A. 1 R. 25 sq. rod cost, at $47.98 per acre ?

14. What will 17 T. 15 cwt. 2 qr. 7 lb. of railroad iron cost, at $47.38 per ton ?

15. How much will 4 lb. 11 oz. 19 dwt. 12 gr. of silver cost, at $13.96 per pound ?

16. What will 428 bu. of oats cost, at $.49 per bushel ?

Suggestion. — At 49 cents per bushel, 428 bushels will cost 428 half dollars, minus 428 cents.

17. How much will 43 volumes cost, at $1.99 per volume ?

18. How much will 48 bbls. of flour cost, at $8.75 per barrel ?

Suggestion. — At $8.75 per barrel, 48 barrels will cost 48 times $9 48 times of a dollar.

19. How much will 32 yds. of cloth cost, at $1.875 per yard?

Suggestion. — At $1.875 per yard, 32 yards will cost 32 times $2 . 32 times s of a dollar.

20. How much will 747 lbs. of tea cost, at $.66per lb. ?

21. How much will 8 cords of wood cost, at $4.94 per cord ?

22. How much will 4 acres of land cost, at $98.75 per acre ?

23. What will 1728 yd. of cloth cost, at 1 s. 8 d. per yard ? Suggestion. 1 s. 8 d. T of £1.

24. What will 857 yd. of broadcloth cost, at 16 s. 8 d. per yard ? Suggestion. 16 s. 8 d. : = £1 3 8. 4 d. = £1 - of £1.

Or, 16 s. 8 d. 10 s. + 6 s. 8 d. = 1 of £1 + f of £1. 25. What will 1478 reams of paper cost, at 13 s. 4 d. per ream ?

Suggestion. 13 s. 4 d. = £1 6 s. 8 d. = £l -- } of £I.

26. What will 737 yd. of black silk cost, at 17 s. 6 d. per yard ?

Suggestion. 2 s. 6 d. = Šof £1.

27. What will 138 yd. of silk velvet cost, at £1 5 s. 6 d. per yard ?

WRITTEN WORK.
a = £138 = cost at £1 per yd.
of a =b= £ 34 10 s. =

" 5 s. per yd.
it of b=c=£ 3 9 s. =

“ 6 d. per yd. a+b+c= £175 19 s. = cost at £1 5 s. 6 d. per yard. 28. What will 13 coats cost, at £3 16 s. 8 d. each?

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4+&=b= £52

6 £4 each.
of a=c= £ 8 13 8. 4 d. = cost at 3 s. 4 d. each.

b

c= £43 6 s. 8 d.

29. What will 24 tons of iron cost, at £8 2 s. 6 d. per ton ?

30. What will 65 pieces of broadcloth cost, at £29 19 s. 8 d. per piece ?

31. What will 45 pieces of Irish linen cost, at £3 1 s. 4 d. per piece ?

32. What will 96 tons of iron cost, at £7 11 s. 4 d. per ton ?

33. If 14 yd. 1 qr. 2 na. 1 in. of cloth cost £12 13 s. 8 d., what will 28 yd. 3 qr. 2 in. of cloth cost ?

Suggestion. 28 yd. 3 qr. 2 in. = twice 14 yd. 1 qr. 2 na. 1 in.

34. If 7 lb. 3 oz. 4 dr. of sugar cost 2 s. 9 d. 1 qr., what will 21 lb. 9 oz. 12 dr. cost ?

35. If 17 bu. 1 pk. 2 qt. of corn cost $9.39, how much will 51 bu. 3 pk. 6 qt. cost ?

36. If 13 gal. 3 qt. 1 pt. 1 gi. of molasses cost $3.87, how much will 41 gal. 2 qt. 1 pt. 3 gi. cost ?

37. If 17 A. 3 R. 7 rd. of land cost $849.29, what will 88 A. 3 R. 35 rd. cost ?

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