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14. If hundred weight of sugar cost 13 dollars 50 cents, what must be paid for 17cwt. 3qrs. 14lb.? Ans. $241.31 cents. 15. How many yards of paper, 2 feet wide, will be required to cover a wall, which is 12 feet long, and 9 fee high? Ans. 14yds. Ift. 2in. 16. If it take 5 men to make 150 pair of shoes in 20 days, how many men can make 1350 pair in 60 days? Ans. 15 men.

17. If a footman travel 240 miles in 12 days, when the days are 12 hours long; how many days will he require to travel 720 miles, when the days are 16 hours long? Ans. 27 days.

18. If 4 men receive $24 for 6 days' work, how much will 8 men receive for 12 days' work? Ans. $96. 19. 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? Ans. $168.

20. A regiment of soldiers, consisting of 800 men, arc to be clothed, each suit containing 4 yds. of cloth, which is 12 yd. wide, and lined with flannel 3 yd. wide; how many yards of flannel will be sufficient to line all the suits? Ans. 8633 yds. 1 qr. 1 na.

PRACTICE.

Practice is a short method of doing all sums in the Single Rule of Thiee, that have one for their first term, and is of great use among merchants.

It may be proved by Compound Multiplication, or by the Single Rule of Three.

Questions to prepare the learner for this rule. 1. What will 50 yards of tape cost at of a cent per yard?

2. What will 40 pounds of beef come to at

per pound?

of a cent

3. What will 100 figs come to at of a cent a piece? 4. How many pence will 40 peaches come to at one farthing a piece?

5. How many shillings and pence will 52 peaches come to at one farthing a piece?

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When the price of one yard, pound, &c. is in furthings.

RULE.

Divide by the aliquot parts of a penny, and the answer will be in pence, which reduce to shillings, pounds, &c.

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CASE II.

When the price is any number of pence less than 12.

RULE.

Divide by the aliquot parts of a shilling, and the answer will be in shillings, which may be reduced to pounds.

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3. What is the value of 237 at 3d.?
4. What is the value of 594 at 4d.?
5. What is the value of 868 at 6d.?
6. What is the value of 988 at 5d.?
7. What is the value of 1049 at 8d.?
8. What is the value of 1294 at 10d.?

CASE III.

£3 14s. Ans.
£ s. d.

Ans. 2 19 3
Ans. 9 18 0
Ans. 21 14 0
Ans. 20 11 8
Ans. 34 19 4
Ans. 53 18 4

When the price in pence exceeds the number of 12,

RULE.

Consider the number given in the sum as containing so many shillings. Then divide by such aliquot parts as may be formed by the pence over a shilling, adding the product to the sum. The answer will be in shillings.

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Note. In this example, I consider the sum as 600 shillings. Then, as the given price is 14d. over a shilling, which makes of a shilling, I divide the sum by 8, and add the quotient to the given sum; which makes 675 shillings, or £33 15s.

2. What is the worth of 450 at 14d.? Ans. £26. 5s. 3. What is the worth of 570 at 16d.? Ans. £38. Os.

CASE IV.

When the price is any number of shillings under 20.

RULE.

Divide by the aliquot parts of a pound, and the answer will be in pounds. Or, consider the sum as being so many shillings, then multiply the sum by the number of shillings in the price. The product will be the answer in shillings; which reduce to pounds.

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The second example is done by the second method, which is thought by many to be the easier way.

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When the price is in pounds, shillings and pence.

RULE.

Multiply the sum or quantity by the number of pounds in the price, then divide the aliquot parts of shillings and pence, and add the quotients to the product-their sum will be the answer.

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Note.-In the second example, after multiplying the sum by the number of pounds, as 4s. is of a pound, I divide by 5, which gives 1135 pounds in the quotient; and leaving a remainder of 3 pounds, which reduced to shillings and divided by 5 give 12s. Then, as 6 and 3 make 9, the number of pence, and as 6d. is of 4s., 1 divide the quotient by 8, which gives 141 pounds with a remainder of 7; this being reduced to shillings, and the 12 shillings above added to it make 152, which divided still by the 8 give 19 shillings. And as 3 is of 6, or its aliquot part, I divide the last quotient hv 2. This gives 70 pounds and a remainder of 1, which is 20 shillings; and adding it with 19 shillings above, the amount is 39 shillings. This divided by the 2 gives 19 shillings and a remainder of 1 shilling, or 12 pence; which divided still by the 2, makes 6d. And thus the answer is obtained.

3. What is the amount of 288 at £5. 10s. 4d.?

Ans. £1588. 16s.

4. What is the amount of 642 at £9. 4s. 6d.?

Ans. £5922. 9s.

5. What is the amount of 734 at £12. 2s. Ed.?

Ans. £8905. 17s. 4d.

CASE VI.

When the quantity consists of different denominations, and the price is in pounds, shillings, &c.

RULE.

Multiply the price of the highest denomination given, by the whole of the highest denomination, then divide by aliquot parts of each of the lower denominations in the Add the results together, and their sum will be

sum.

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