9. What will a merchant gain by buying 436 yards of linen, at 8.5s. per yard, and selling it at 10.75s. per yard? Ans. 49 L. 1s.

10. A grocer bought 7.6 cwt. of sugar, at 40.1 s. per cwt. and retailed it out at 4.5d. per lb. Whether did he gain or lose, and how much?

Ans. He gained 14s. 5d. 1.12 qrs.

11. A. bought 3 cwt. 1.5 qr. of cloves, at 2.75s per lb. which he afterward sold for 60 L. 11s. 6d. How much did he gain by the transaction? Ans. 8L. 12s.

12. If 1 yard of ribbon sell for 4.5 cents, how much will 345 yards bring? Ans. 15.525 dols. Or $15.521

INVERSE PROPORTION.

1. How long will 3 men be in performing a piece of work which will occupy 5 men 40.5 days?

As 5 40.5 :: 3 : 67.5 Ans.

2. How many men can do as much work in .4 of a month, as 16 can do in 1.5 month?

Ans. 60. 3. How much silk .75 of a yd. wide, will line 25.5 yards of cloth that is 5 qrs. wide? Ans, 42.5 yds. 4. If a board be .75 of a foot bread, what length must it be to measure 12 feet square?

5. A. had 40.7 yards of linen, for 25.6 ells of holland, at 4.5s. per cll. linen per yard?

Ans. 16 feet. which B. gave him How much was the Ans. 2s. 9d. 3.8qrs.

THE DOUBLE RULE OF THREE,

IN DECIMALS.

Questions in this rule are wrought as in whole numbers, placing the points agreeably to former directions.

EXAMPLES.

1. If 3 men receive 8.9 L. for 19.5 days labour, how much must 20 men have for 100.25 days?

2. If 2 persons receive 4.625s. for 1 days labour, how much should 4 persons have for 10.5 days?

Ans. 4L. 17s. 1d.

3. If the interest of 76.5 L. for 9.5 months, be 15.24 L. what sum will gain 6 L. in 12.75 months?

Ans. 22 L. 8s. 93d.

4. How many men will reap 417.6 acres in 12 days, if 5 men reap 52.2 acres in 6 days? Ans. 20 men.

5. If a cellar 22.5 feet long, 17.3 feet wide, and 10.25 feet deep, be dug in 2.5 days, by 6 men, working 12.3 hours a day; how many days of 8.2 hours, should 9 men take to dig another, measuring 45 feet long, 34.6 wide, and 12.3 deep? Ans. 12 days.

ALLIGATION.

Alligation is a rule for adjusting the prices and simples of compound quantities.

CASE 1.

To find the mean price of any part of the composition, when the several quantities and their prices are given.

RULE.

As the sum of the several quantities,

Is to their total value;

So is any part of the composition,

To its value.

PROOF.

The value of the whole mixture at the mean price must agree with the total value of the several quantities at their respective prices.

EXAMPLES.

1. If 6 gallons of wine at 67 cents per gallon, 7 at 80 cents, and 5 at 120 cents per gallon be mixed together, what will 1 gallon of the mixture be worth?

*

2. If 19 bushels of wheat at 6s. per bushel'; 40 bushels of rye at 4s. per bushel; and 12 bushels of barley, at 3s. per bushel, be mixed together, what will a bushel of the mixture be worth? Ans. 4s. 41d.

3. If a grocer mix 2 cwt. of sugar at 56s. per cwt.; 1cwt. at 43s. per cwt.; and 2 cwt. at 50s. per cwt. what will be the value of 1 cwt. of the mixture? Ans. 2 L. 11s.

4. A farmer mingled 20 bushels of wheat at 5s. per bushel, and 36 bushels of rye at 3s. per bushel, with 40 bushels of barley at 2s. per bushel; I desire to know the worth of a bushel of this mixture? Ans. 3s.

5. If 4 ounces of silver worth 75 cents per ounce, be melted with 8 ounces worth 60 cents per ounce, what will 1 ounce of the mixture be worth? Ans. 65 cents.

6. A wine merchant mixes 12 gallons of wine at 4s. 10d. per gallon, with 24 gallons at 5s. 6d. and 16 gallons at 6s. 31d.; what is a gallon of the mixture worth?

CASE 2.

Ans. 5s. 7d.

When the prices of several simples are given, to find how much of each, at their respective rates, must be taken to make a compound or mixture at any proposed price.

RULE.

Write the rates of the simples under each other, and link each rate which is less than the mean rate, with one or more that is greater; place the difference between each rate and the mean price, opposite to the rates with which it is linked; then if only one difference stand against either rate, it will be the quantity required at that rate; but if there be several, their sum will be the quantity.

Note 1.-If all the given rates be greater, or less, than the mean rate, they must be linked to a cipher.

2. Different modes of linking will produce different an

swers.

EXAMPLES.

1. How much rye at 4s. per bushel, barley at 3s. per bushel, and oats at 2s. per bushel, will make a mixture worth 2s. 6d. per bushel?

2. A vintner has three kinds of wine, viz. one kind at 160 cents per gallon, another at 180 cents, and another at 240 cents; how much of each kind must he take to make a mixture, worth 190 cents per gallon?

Ans.

{

50 gals. at 160 cts. 50 gals. at 180 cts. and 40 gals. at 240 cts.

3. How much sugar at 4d. at 6d. and 11d. per lb. must be mixed together to make a composition worth 7d. per lb. Ans. An equal quantity of each kind.

4. It is required to mix several sorts of wine, viz. at 9s. 15s. and 21s. per gallon, with water, that the mixture may be worth 12s. per gallon; how much of each sort must be taken? *

Ans.

3 gals. at 9s. 3 gals. at 15s. and 12 gals.

1

at 21s. with 9 gals. of water.

5. A grocer has several sorts of sugar, viz. one sort at 12 cents per lb. another at 11 cents, a third at 9-cents, and a fourth at 8 cents per lb.; how much of each sort must he take to make a mixture worth 10 cents per lb. ?

CASE 3.

. When the price of all the simples, the quantity of one of them, and the mean price of the whole mixture are given, to find the several quantities of the rest.

RULE.

Link the several prices and place their differences as in case 2; then

As the difference opposite to the price of the given quantity,

Is to the given quantity;

So are the differences respectively,

To the several quantities required.

EXAMPLES.

1. A grocer would mix 30 lb. of sugar, at 14 cents per lb. with some at 9 cents, 10 cents, and 13 cents per lb. ; how much of each sort must he mix with the thirty lb. that the mixture may sell at 12 cents per lb. ?

2. How much barley at 30 cents per bushel, rye at 36 cents, and wheat at 48 cents, must be mixed with 12 bushels of oats, at 18 cents, to make a mixture worth 22 cents per bushel? Ans. 1 bushel of each sort.

3. How much wine at 5s. at 5s. 6d. and at 6s. per gallon, must be mixed with 3 gallons at 4s. per gallon, so that the mixture may be worth 5s. 4d. per gallon?

Ans. 3 gals. at 5s., 6 at 5s. 6d., and 6 át 6s. 4. How much tea at 12s. 10s. and 6s. per lb. must be mixed with 20 pounds at 4s. per lb. to make a mixture worth 8s. per lb. ?

Ans. 10 lb. at 6s., 10 lb. at 10s., and 20 lb. at 12s.

CASE 4.

When the prices of the several simples, the quantity to be compounded, and the mean price are given, to find the quantity of each simple.