10. There was a certain edifice completed in a year by 20 workmen; but the same being demolished, it is necessary that just such a one should be built in 5 months. I demand the number of men to be employed about it.

Ans. 48 men.

11. If the freight of 9 hhds. of sugar, each weighing 12 cwt., 20 leagues, cost £16, what must be paid for the freight of 50 tierces, each weighing 23 cwt., 100 leagues? Ans. £92 11 s. 103 d. 12. If 950 soldiers consume 350 quarters of wheat in 7 months, how many soldiers will consume 1464 quarters in 1 month? Ans. 27816 soldiers.

13. If 1464 quarters of wheat be used by 27816 soldiers in a month, in what time will 950 soldiers consume 350 quarters? Ans. 7 months. 14. If $100 gain $6 in a year, what will $400 gain in 9 months? Ans. $18. 15. If $100 will gain $6 in a year, in what time will $400 gain $18? Ans. 9 months.

XXIII. Value of Compounds or Mixtures.

TO FIND THE MEDIUM PRICE OF SEVERAL ARTICLES MIXED, THE QUANTITY AND VALUE OF EACH BEING GIVEN.

RULE.-Divide the whole cost of the articles by the sum of the articles, and the quotient will be the medium price of one article.

1. A grocer mixed 2 cwt. of sugar, at $9 per cwt. and 1 cwt. at $7 per cwt. and 2 cwt. at $10 per cwt.; what is the value of 1 cwt. of this mixture?

2. If 3 pounds of gold, of 22 carats fine, be mixed with 3 pounds, of 20 carats fine; what is the fineness of the mixture?

22X3-66
20×3=60

6|126

Ans. 21

3. If I mix 10 lbs. of sugar, worth $,1 per lb.; 8 lbs. worth $,12; 20 lbs. worth $,14; what must I charge per pound of the mixture? Ans. $,1259.

TO FIND WHAT QUANTITY OF EACH OF THE INGREDIENTS WHOSE RATES ARE GIVEN, WILL COMPOSE A MIXTURE OF A GIVEN RATE.

RULE. Place the several prices of the ingredients in a column under each other, the least uppermost, and so on, downward, according to their value.

Connect, with a continued line, the price of each ingredient which is less than the rate of the compound, with one which has a greater value than the compound. Place the difference between the mean price, or rate of the compound, and that of each ingredient, opposite to the rates with which they are connected. If only one difference stand against any rate, it will be the quantity belonging to that rate; but if there be several, their sum will be the quantity.

1. A merchant has spices, some at 1 s. 6 d. per lb., some at 2 s., some at 4 s., and some at 5 s. per lb.; how much of each sort must he mix, that he may sell the mixture at 3 s. 4 d. per lb.?

By connecting the less rate with the greater, and placing the difference between them and the medium rate alternately, or one after the other in turn, the quantities resulting are such that there is precisely as much gained by one quantity as is lost by the other, and therefore the gain and loss, upon the whole, are equal and exactly the proposed rate. Various answers arise from the different modes of uniting the rates of the ingredients.

2. How much wine, at 6 s. per gallon, and at 4 s. per gallon, must be mixed together, that the compound may be worth 5 s. per gallon? Ans. 1 gal. of each.

3. How much corn, at 2 s. 6 d., 3 s. 8 d., 4 s., and 4 s. 8 d. per bushel, must be mixed together, that the compound may be worth 3 s. 10 d. per bushel?

Ans. 12 at 2 s. 6 d.,

4 s. 8 d.

12 at 3 s. 8 d., 18 at 4 s., and 18 at

TO FIND THE SEVERAL QUANTITIES WHEN ONE OF THE INGREDIENTS IS LIMITED TO A CERTAIN QUANTITY.

RULE. Find the differences between the medium rate and the price of each ingredient, according to the preceding rule. Then say, as the difference of that simple, whose quantity is given, is to the rest of the differences severally, so is the quantity given, to the several required quantities.

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

Ans. 3 gal. at 5 s., 6 at 5 s. 6 d., and 6 at 68.

2. A grocer would mix teas at 12 s., 10 s., and 6 s., with 20 lb. at 4 s. per lb.; how much of each sort must he take to make the compound worth 8 s. per lb. ?

Ans. 20 lb. at 4 s., 10 lb. at 6 s., 10 lb. at 10 s., and 20 lb. at 12 s.

то FIND THE SEVERAL QUANTITIES WHEN THE WHOLE COMPOUND IS LIMITED TO A CERTAIN QUANTITY.

RULE. Find the proportional quantities, and then say, as the sum of the proportional quantities, or differences, is to the given quantity, so is each proportional quantity, or difference, to the required quantity of each.

1. How many gallons of water must be mixed with wine worth 3 s. per gallon, so as to fill a vessel of 100 gallons, and that a gallon may be afforded at 2 s. 6 d.?

2. A grocer has currants at 4 d., 6 d., 9 d., and 11 d. per lb., and he would make a mixture of 240 lb. so that it might be afforded at 8 d. per lb.; how much of each sort must he take?

Ans. 72 lb. at 4 d., 24 lb. at 6 d., 48 lb. at 9 d., and 96 lb. at 11 d.

XXIV. Partnership.

The object of this section is to estimate the gain or loss of individuals doing business in partnership. The processes here given, hardly require a separate consideration; but in conformity to long-established usage, rather than from a conviction of propriety, a method of working partnershipsums is given.

TO FIND THE SHARE OF GAIN OR LOSS OF EACH INDIVIDU-

AL, WHEN HIS SHARE IS EXPRESSED BY A FRACTION.

RULE. Reduce the fractions to the same denominator, and divide the whole gain or loss by the denominator, and multiply the quotient by each numerator, and the several products will be the several answers.

1. A and B companied, and trade with a joint capital of $400; A receives, for his share of the gain, one half as much as B; what was the stock of each?

It is plain that A receives, and B. Therefore, divide $400 by the denominator 3, and multiply by the numerators. $400÷3=A's $1334×2=B's 2663.

2. Divide $125 between two men in such a manner that one shall have more than the other, after the sum is divided. Ans. One has $50, and the other $75.

TO FIND THE SHARE OF GAIN OR LOSS WHEN EACH INDIVIDUAL IS TO RECEIVE ACCORDING TO HIS STOCK IN TRADE.

RULE.-Divide the whole gain or loss by the whole stock in trade, and multiply the quotient by each man's share of the stock.

When the whole gain or loss is divided by the whole stock in trade, the quotient is the gain or loss on one dollar. Then the gain or loss of each man will be found by multiplying the gain or loss on one dollar by the number of dollars which constitute his share.

1. A, B, C, and D are concerned in a joint stock of $1000, of which A's part is $150, B's $250, C's $275, and D's $325. Upon the adjustment of their accounts, they have lost $337,5. What is the loss of each?

337,5÷1000=,3375, loss on one dollar.