12. In 100 volumes of air there are 21 volumes of oxygen and 79 of nitrogen. How much of each is there in a room 18 ft. by 16 ft. by 15 ft.?

13. Type-metal is composed of 39 parts of lead and 11 parts of antimony. How many pounds of each in 400 lb. of type?

14. Bell-metal contains 78 parts of copper to 22 parts of tin. How much of each in a bell weighing 245 lb.?

15. Divide $72 among James, John, and Henry so that John shall have 3 times as much as James, and Henry as much as James and John together.

SOLUTION.-Let 1 represent James's part, then

3 represents John's part, and

4 represents Henry's part.

Hence James has of $72, or $9; John, of $72, or $27; and Henry, of $72, or $36.

16. In a load of 272 pumpkins, melons, and gourds there are twice as many melons as pumpkins, and 4 times as many gourds as melons and pumpkins together. How many of each ?

17. It is 728 feet from A to E. The distance from B to C is five times the distance from A to B ; from C to D is 2 times the distance from A to C ; and from D to E is 14 times the distance from B to D. How far is it from A to B ; B to C? etc.

PARTNERSHIP.

437. A partnership is an association of two or more persons for the transaction of business.

A partnership association is called a company, firm, or house; the members of it, partners; and the property invested in the business by the partners, capital, joint stock, or stock in trade.

When the capital or property of the partners is invested an equal time, the partnership is called simple: when their capital is invested an unequal time, the partnership is called compound.

1. A, B, and C entered into partnership for 1 yr.; A put in $450, B $540, and C $720, and their net profits were $380. What was each partner's share?

PRINCIPLE.-In simple partnership the gain or loss is shared by the partners in proportion to the amounts of their capital.

EXERCISES (Written).

438. 1. B and C were partners in business for 4 years; B put in $3600 and C $4200, and their profits were $910. What was each partner's share of the profits?

2. James caught 25 fishes, William 35, and Thomas 15, and they sold them all for 60 cts. How much of the money should each receive ?

3. A, B, and C formed a partnership in business ; A put in $7000, B $5600, and C $4284, and their loss was $536. What was each partner's share of the loss?

4. The capital of two partners is proportional to 5 and 4, and their profits are $990. What is the share of each ?

5. The capital of four partners is proportional to 23, 24, 31, and 3%, and their profits are $1000. What is each partner's share?

6. Frank and Moses sold 2 baskets of apples at a profit of 20 cts. each. Frank owned of the apples in the first basket, and Moses of those in the second. To how much of the gain is each entitled ?

7. A and B traded in partnership 2 years, making an annual profit of $3240; during the first year A owned & of the stock, and during the second year B owned § of it. What is each partner's share of the total profits?

8. Three partners, A, B, and C, furnish capital as follows: A, $300 for 5 mo.; B, $450 for 4 mo.; C, $350 for 6 mo. They gain $270. What is each partner's share?

EXPLANATION.-The use of $300 for 5 mo. is the same as the use of $1500 for 1 mo. ; the use of $450 for 4 mo. is the same as the use of $1800 for 1 mo. ; and the use of $350 for 6 mo. is the same as the use of $2100 for 1 mo. We now divide the gain, $270, into parts proportional to $1500, $1800, and $2100, as these represent the amounts invested by the partners for equal times.

PRINCIPLE.—In compound partnership, the gain or loss is shared by the partners in proportion to the products of the amounts of their capital by the time of investment.

9. A and B enter into partnership. A puts in $650 for 8 mo.; B, $775 for 12 mo., and their profits are $377. Find the share of each.

10. The amounts invested by two partners are proportional to 6 and 8; the capital of the first is in trade 5 mo., and that of the latter 6 mo. If they gain $1111, what will be the share of each ?

11. In a partnership for 1 yr., A at first put in $5000, and 4 mo. after $2000 more; B at first put in $6000, and 6 mo. after withdrew $1500; and C at first put in $3000, and 9 mo. after put in $4000 more. The whole gain was $4500. What

was the share of each ?

12. A, B, and C entered into partnership Jan. 1, with a joint capital of $7200, of which A owned , B, and C the remainder. June 1, A decreased his capital by, Aug. 1, B increased his capital by, and Oct. 1, C increased his capital by 3. The net profits for the year were $2370. Find the share of each.

MIXTURES.

439. To find the average price of a mixture of different articles, when the quantity of each article and its price are given.

1. A grocer mixes 20 lb. of sugar, worth 15 cts. per lb., with 24 lb. worth 10 cts., and 28 lb. worth 9 cts. What is a pound of the mixture worth?

Hence 1 lb. of the mixture = $7.92 72, or 11 cts.

RULE. Find the value of each article, and divide the total value by the number of articles.

EXERCISES (Written).

440. 1. If a mixture be made of 8 lb. of candy, worth 15 cts. a pound, 12 lb. worth 20 cts., and 20 lb. worth 25 cts., what will one pound of it be worth?

2. If 20 lb. of tea, worth 40 cts. a pound, 30 lb. worth 60 cts., 40 lb. worth 32 cts., and 60 lb. worth 38 cts., be mixed together, what will the mixture be worth per pound?

3. A man bought 30 acres of land, @ $5; 15 acres, @ $7; and 35 acres, @ $6.40. What was the average price per acre?

4. If 18 gallons of whisky worth $2.50 per gallon, and 28 gallons worth $3, are mixed with 14 gallons of water, which cost nothing, what is a gallon of the mixture worth?

5. A thermometer stood, from 6 to 9 A.M., at 65°; from 9 to 11 A. M., at 74°; from 11 A. M. to 2 P. M., at 80°; and from 2 to 6 P.M., at 78°. What was the average temperature of the day?

441. To find what proportions of several articles of different values are required to form a compound of a particular value.

1. A grocer has sugar worth 6 cts., 7 cts., 12 cts., and 13 cts. a pound, which he wishes to mix together so as to form a mixture worth 9 cts. a pound. What proportions of the different sugars must he take?

EXPLANATION.-In selling the sugars which are worth less than 9 cts. for 9 cts., there will be a gain; and in selling those which are worth more than 9 cts. for 9 cts., there will be a loss. Now, we desire to take such amounts of each that the gain will balance the loss.

OPERATION.

cop

(1) (2) (3)

(4) (5)

6

3

4

3 3

9

12

2

2

13

3

On 1 lb. of the 6-ct. sugar there will be a gain of 3 cts. ; hence, on

On 1 lb. of the 13-ct. sugar there

a lb. there will he a loss of 1 ct.

of a lb. there will be a gain of 1 ct. will be a loss of 4 cts. ; hence, on of That is, if we take of a lb. of the 6-ct. sugar as many times as we take of alb. of the 13-ct. sugar, the gain and loss will be exactly equal. Hence we write and in the 1st column for the proportional amounts to be taken of the sugars whose prices they stand opposite.

In the same manner we find the proportional amounts and for the 7-ct. and 12-ct. sugars, which we write in the 2d column.

Now, since we may take any number of times, provided we also take the same number of times, we may multiply them by 12, the L. C. M. of their denominators, and thus reduce them to 4 and 3, which we write in the 3d column. Similarly, multiplying and by 6, we obtain 3 and 2, which we write in the 4th column. Hence the required proportional amounts are 4lb. of the 6-ct. sugar, 3 lb. of the 7-ct., 2 lb. of the 12-ct., and 3 lb. of the 13-ct., which proportional numbers we write in the 5th column.

It is evident that problems of this kind may have an unlimited number of sets of answers; for any multiple of the proportional numbers found also expresses the proportional quantities to be taken of each.