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S.

S.

lbs.

27 18 :: 9

9

Example 1.-If 9 lbs. of tea cost 27s., how many lbs. may be purchased for 18s.? State and work the question as follows:Here the answer wanted is lbs.: the 9 lbs., therefore, are made the third term; and since a less quantity will be bought for 18s. than for 27s., the answer will be less than the third term; therefore 18s., the lesser of the other two terms, is made the second, and 27s., the greater, the first: then multiplying the second and third terms together, we have 162, which, divided by 27, give

27) 162

Ans. 6 lbs.

6 lbs. for the fourth or previously unknown term.

Example 2.-If 12 men can execute a piece of work in 18 days, how long will 3 men take to do the same?

Men. Men. Days. 3: 12 : 18

12

3)216

Ans. 72 days.

In this example the answer wanted is days, the 18 days are therefore made the third term; and as 3 men will take longer than 12 men to execute the work, and the answer should consequently be greater than the third term, the greater of the other two is placed second, and the lesser first.

Example 3.-If 1 cwt. 1 qr. 6 lbs. of sugar cost £3, 6s. 11d., what will 2 cwts. 3 qrs. 5 lbs. cost?

cuts. qrs. lbs. cwts. qrs. lbs. £ S. d.

1 1 6

2 3 5 :: 3 :

6

11

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Here, in order to make the first term a simple number, it is reduced to its lowest denomination, namely, Ibs.: the second term is therefore reduced to lbs. also, that both may be alike. The third term is reduced to its lowest denomination, pence. After multiplying and dividing, according to rule, the quotient is 1721 pence, and a remainder of 73d.: these being further reduced to farthings, and divided by the first term, give 2 farthings, which are placed in the quotient: then convert the 1721 d. into pounds, &c., and the answer is £7, 3s. 54d.

CONTRACTION OF THIS RULE.-The working of the questions may often be much shortened as follows:

Divide the two first terms, or the first and last terms (but never the second and third) by any number that will divide both without a remainder; then proceed according to the rule, with the quotients, instead of the original terms which are now said to be cancelled-a stroke being drawn across them to indicate this.

The cancelling does not alter the relative proportion between the two terms, because both have been divided by the same number, and the answer to the question will be the same as if the original terms had been employed; whilst, from the terms having been lessened, the calculations are more easily performed.

Example 1.-If 15 yards cost £9, 12s., what will 55 yards cost?

£ S. d.
12 0

yas. yds.
15 55 :: 9

3 11

11

3)105 12 0

£35 4 0 Ans.

Here the first two terms are divided by 5, and the quotients employed instead of the original terms, which are cancelled.

See Note as to the multiplication of the third term, p. 56.

Example 2.-If 5 lbs. cost £1, 7s. 6d., what will 45 lbs. cost?

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Example 3.-If 34 yds. cost £4, 8s., how much will 11s. purchase?

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Example 4.-If 7 yards cost 28s., how much will £5, 3s. purchase?

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Example 5.-If 7 yards cost 28s., what will 26 yards cost?

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ANOTHER METHOD OF STATING THE TERMS IN PROPORTION.Instead of stating the terms according to the rule, as given at page 56, it will often be found simpler to state them in the following order-the working of the question being the same as before :

I. WHEN the greater of the two similar terms requires the greater answer, or the lesser requires the less answer.

RULE. Write down the terms in the order in which the sense can be plainly expressed in words, making that the middle term which is of the same kind as the answer required: then, as before, multiply the two last terms together, and divide the product by the first. The answer will be of the same kind as the middle term.

The terms may be cancelled, when practicable, as already explained.
Example.-If 10 yards of cotton cost 20s., what will 30 yards cost?

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The reason for multiplying and dividing is as follows:-The price of 10 yards being 20s., if we divide 20 by 10, we will get the price of 1 yard-namely, 2s.: if we then multiply the price of one yard by 30, we will get the price of 30 yardsnamely, 60s. In practice, we multiply before dividing, as it is usually more convenient.

II. WHEN the greater of the two similar terms requires a less answer, or the less requires a greater answer.

RULE.-State the two similar terms in the inverse order in which they are stated by Rule I. Thus-first suppose the question to be stated according to the meaning, as in Rule I., then reverse the terms, placing the first as the third, and the third as the first.

Example.-If 12 men take 18 days to execute a piece of work, how many days will 3 men take?

Men. Days. Men.

3: 18 :: 12 12

3)216

Ans. 72 days.

By Rule I., this would be stated-12: 18 :: 3; but as the smaller number of men, 3, will require the greater answer, the 3 is placed first, and 12 last.

Exercises.

1. If 4 yds. of linen cost 10s., what will 16 yds. cost? Ans. £2. 2. If 6 lbs. of tea cost 26s. what will 28 lbs. cost? Ans. £6, 1s. 4d. 3. I paid Sd. for 2 oz. of tea; what is that per lb. ?" 5s. 4d. 4. If 15 yards of cloth cost £10, what is the value of 3 yards? Ans. £2.

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5. If for 10s. I can buy 4 yards of linen, how much can I purchase for 40s. ? Ans. 16 yards.

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6. If I pay 20s. for 28 lbs. of sugar, how much may be had for 5s.?

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7. If 10 men can do a piece of work in 8 days, 4 men take to do the same?

8. If a piece of work can be done in 16 days many men must be employed to do it in 4 days?

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Ans. 7 lbs. how long will Ans. 20 days. by 6 men, how Ans. 24 men.

9. If 45 yards of cloth cost £18, 14s. 6d., what will 9 yards cost? Ans. £3, 14s. 10d.

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10. If 8 oz. of silver-plate cost £2, 16s., what will 3 lbs. 4 oz. cost? Ans. £14. 11. A lady went to a china-shop and purchased 19 dinner-plates, for which she paid 9s. 6d.; at what rate per dozen did she buy the plates? Ans. 6s. 12. A gentleman paid an account for 2300 feet of gas, supplied by meter, amounting to 19s. 6d. ; at what rate, per 1000 feet was the gas charged? Ans. 8s. 5d. 23 13. What does a servant's wages amount to in 13 weeks, at the rate of £25 a year?

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Ans. £6, 5s. 14. How much cloth, at 12s. 6d. per yard, should be given in exchange for 85 lbs. of tea, at 5s. 4d. per lb.? Ans. 36 15. Bought 13 cwts. 3 qrs. of flax, at £65 amount to?

16. What will 3 cwts. 2 qrs. 7 lbs. of 12s. 6d. per stone of 14 lbs. ?

17. If the yearly rent of a farm of should be the rent of 63 acres?

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18. If 36 reams of paper cost £28, reams cost? 19. Find the value of 13 cwts. 3 qrs. 18 per cwt.,

yards.

per ton; what did it Ans. £44, 13s. 9d. butter amount to, at

Ans. £17, 16s. 3d. acres be £320, what Ans. £73, 0s. 104d. 13 15s., how much will 150

20. A piece of blue cloth, measuring 65 what is the value of 34 yards?

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Ans. £119, 15s, 10d. lbs. of sugar, at 76s. 8d.

Ans. £53, 6s. 53d. yards, cost £43, 15s.; Ans. £2, 3s. 9d.

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Ans. 16

21. If 10 yards of linen be required for 3 shirts, how many will a piece containing 53 yards make? shirts. 22. How much linen will be required for 18 shirts, if 3 require 10 yards?. Ans. 63 yards.

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23. How much will 4 casks of butter cost, each weighing 44 lbs., at the rate of 12s. 6d. per stone of 14 lbs.? Ans. £7, 17s. 11d. & 24. A piece of cloth 8 yards long cost £4, 16s., how much at that rate would a piece 42 yards long cost? Ans. £25, 4s.

25. Paid 8s. 9d. for dyeing a piece of silk 7 yards long; how much will a piece 26 yards long cost at the same rate?

Ans. £1, 12s. 6d. 26. If it require 5 reams of paper to print 100 copies of a book, how much will be wanted for an edition of 3500 copies ?

Ans. 175 reams.

27. If I pay £5, 15s. for a piece of cloth measuring 20 yards, how much will 3 yards cost? Ans. 17s. 3d.

28. If 6 silver tea-spoons weigh 4 oz., how much silver will there be in 3 doz.? Ans. 2 lbs. 3 oz.

29. A ship is provisioned for 60 days, allowing each man 3 lbs. a day; how much should be allowed to make these provisions last 80 days? . Ans. 24 lbs. 30. If 18 persons can reap a field in 10 days, how many must be employed to do it in 4 days? Ans. 45 persons.

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31. If 5 yards of cloth cost £3, 17s. 6d., what will 12 yards cost?

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32. If I pay £1, 18s. for 2 yards of cloth, purchase for £5, 14s.?

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Ans. £9, 4s. 6d. how much can Í Ans. 74 yards.

33. What should be paid for 14 lbs. of sugar, at the rate of £3, 14s. 8d. per cwt.?

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Ans. 9s. 4d.

34. If a piece of muslin, measuring 16 yards, cost 26s. 8d., how much should 6 yards of it cost? .

Ans. 10s. 35. What will 9 cwts. 2 qrs. 15 lbs. of sugar amount to, at the rate of 35s. 6d. per 50 lbs. ? Ans. £38, 6s. 1d.

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Ans. 13s. 112d. #

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36. Find the price of 16 lbs. of butter, at the rate of £4, 17s. 6d. per cwt., 37. What is the price of 12 lbs. of coffee, when a cwt. cost £9, 15s.? Ans. £1, 0s. 101d. 38. Find the cost of a cheese, weighing 244 lbs., at £3, 6s. 8d. per cwt., Ans. 14s. 7d. 39. A hogshead of sugar, weighing net 13 cwts. 1 qr. 17 lbs., amounted to £48, 7s. 7d.; what is the price per cwt.? Ans. £3, 12s. 24d. 781 40. What is the value of 3 cwts. 1 qr. 18 lbs. of flax, at £73, 15s. per ton?. Ans. £12, 11s. 6d. 13 41. What will a piece of cloth, measuring 27 yds. 3 qrs. amount to, if 2 yds. 1 qr. 3 nails of the same cost £1, 12s. 8d.? Ans. £18, 11s. 103d. 42. Find the value of 10 qrs. 5 bushels of wheat, at 8s. 9d. per bushel, 43. How much wheat may be bought for £100, when the price is 72s. 6d. per quarter? Ans. 27 quarters. cwts. 3 qrs. 22 lbs.,

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Ans. £37, 3s. 9d.

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44. Bought a lot of tobacco, weighing 87 for £576, 17s. 8d.; what did it cost per cwt.? Ans. £6, 11s. 24d. 523 45. If I pay 21s. 8d. for 5 lbs. of tea, what quantity at the same rate will come to £18, 19s. 4d.? Ans. 87 lbs.

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46. In sowing a field with wheat, it was found that it required 2 pecks for every 3 roods; how much did it take for the whole field, which measured 7 acres 2 roods 30 poles? Ans 20 pecks. 47. Bought a piece of linen, containing 54 yards, for £5, 16s. 8d., gave a friend at his request 16 yards; what should he pay me for that quantity? Ans. £1, 14s. 6d. 48. If 14 lbs. of iron cost 3s. 74d., how much iron may I purchase for £21, 4s. 1d.? Ans. 14 cwts. 2 qrs. 14 lbs. 49. What is the price of 3 pieces of scarlet, each 57 yards, when 76 yards cost £72, 3s. 44d.? Ans. £162, 7s. 6d. 50. What is the price of 5 boxes of tea, each containing 37 lbs., at £4, 13s. 9 d. for 17 lbs. ? Ans. £51, 0s. 103d.

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51. How much will 41 yards 2 qrs. amount to at £22, 17s. 6d. for 25 English ells? Ans. £30, 7s. 6d. 2

52. If the rent of 82 acres 3 roods 20 poles be £241, 17s. 2 d., how much will the rent of 10 acres 1 rood amount to at the same rate? Ans. £29, 18s. 32d. 4

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