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2. Separate $24,000 into parts proportional to 3, 4, and 5. 3. Separate $36,000 into parts proportional to 3, 5, and 10. 4. The total receipts of a coal mining company one year were $16,725,000, and the expenses were to the net earnings as 13 is to 2. What were the expenses? the net earnings?

5. The daily ration of a German soldier in the field weighs 1300 grams and consists of bread, meat, rice, salt, and coffee in the proportion 6:3:1::. Find the weight of each.

6. The freight earnings of two railroads on a train load of grain were $2160. One carried the grain 400 miles, the other 500 miles. Find the earnings apportioned to each road.

7. The annual earnings of a certain railroad company are $78,000,000. Find the amounts received from freight charges, from passenger service, and from other sources (such as mail, express, etc.), if they are in the proportion 8:4: 1.

8. A quarterly dividend of $6412.50 was divided among the 8 shareholders of a corporation. The holdings of the shareholders were 30, 15, 24, 18, 48, 36, 42, and 72 shares, respectively. What sum did each shareholder receive?

PARTNERSHIP

509. When two or more persons agree to combine their money, goods, labor, or skill, in some business enterprise, and to share the profits and losses of the business in certain proportions, they become partners, thus forming a partnership.

The partners are collectively called a firm, or a house.

510. As a rule the legal liability of a partner in a firm is different from that of a stockholder in a company or corporation; for while a stockholder is liable, with few exceptions, for only the par value of his holdings, a partner is usually liable for the entire indebtedness of the firm.

511. The investment of a partner is called his capital.

The capital may be money or anything that has a money value in the business, as goods, labor, skill, experience, the "good will" of the trade, or some mercantile advantage, etc.

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512. The gains and losses of a firm are shared in proportion to the amount of capital invested by each, and the length of time such capital is invested in the business.

WRITTEN EXERCISES

513. 1. A and B engaged in business as partners and gained $4000. A's capital was $10,000, and B's was $6000. Find the profits apportioned to each.

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2. A and B owned a strawboard factory, A's investment being $75,000 and B's $45,000. The net earnings for one year were $11,200. How much of the earnings did each partner receive?

3. Apportion a loss of $2400 to the three partners in a business, if their respective investments are $11,000, $ 15,000, and $6000.

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4. A business block worth $28,000, owned by three men, was insured for of its value. One had $16,000 invested, one $7000, and one $5000. The block was completely destroyed by fire. What was the amount of insurance due each man? 5. As the result of a damage suit, a judgment for $4600 was obtained against the joint owners of a quarry. The owners' investments were $10,000, $3000, $ 6500, and $ 3500, respectively. How much was each owner obliged to pay?

6. Three men invested $2200, $1800, and $2000, respectively, in a business. After several years, during which the business had grown to $10,500, the first partner withdrew from the firm. How much was his share worth?

The other two bought his part in proportion to their holdings. How much did each pay?

7. Four partners with a capital of $48,000, of which A, B, and C furnished $10,000 each and D the rest, declared a 16% dividend and used the surplus profits, $2880, to increase their capital. Find each partner's dividend and his increased capital.

8. A and B formed a partnership with a capital of $8000, of which A furnished $5000. After 18 months A withdrew $1000, and at the end of 2 years the partnership was dissolved. If the gain for 2 years was $7440, how much did each partner receive?

A's gain

=

SOLUTION

A's capital, $5000 for 18 mo. = $90000 for 1 mo.

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$4000 for 6 mo. = $ 24000 for 1 mo.
A's total capital
= $114000 for 1 mo.

B's capital, $3000 for 24 mo. = $ 72000 for 1 mo.
Total investment for both = $186000 for 1 mo.

186000

=

186000

114000 of $7440 = $4560; B's gain 72000 of $7440 = $2880. Test. $4560 + $2880

=

$7440.

9. A and B were partners and divided $3075 in profits. A's investment was $5000 for 1 year; B's was $5000 for 9 months and $6000 for 3 months. How much did each receive?

10. A and B began business with a capital of $10,000, g of which A furnished. After 6 months C entered the firm with a capital of $5000. After another 6 months they divided $5500

in profits. How much did each partner receive?

11. A, B, and C were partners for 16 months. A contributed $30,000, B $20,000, and C $40,000, $15,000 of which he withdrew in 12 months. When they dissolved partnership they divided $41,400 in profits. Find the profits allotted to each.

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What is the product when 2 is taken 2 times as a factor? 3 times? 4 times? 5 times? 6 times?

What is the second power of 2? the third power of 2? the fourth power? the fifth power? the sixth power?

2. What number is the second power of 3? the third power of 3? the fourth power?

3. Find the second power of 10; the third power.

515. The number of times a number is to be used as a factor may be indicated by using an exponent (§ 118).

516. The product arising from using a number a certain number of times as a factor is called a power of that number.

4 is the second power of 2, for 4 = 2 × 2, or 22; 8 is the third power of 2, for 8 = 2 × 2 × 2, or 28; 16 is the fourth power of 2; etc.

A number is regarded as the first power of itself.

517. If the side of a square is 2, the area is the second power of 2; if the side is 3, the area is the second power of 3; etc.

Therefore the second power of a number is called its square.

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If the edge of a cube is 2, the volume is the third power of 2; if the edge is 3, the volume is the third power of 3; etc.

Therefore the third power of a number is called its cube.

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1 2 2 3 4 5 6 7 8 9 10

2. Find the cube of 1; of 2; of 3; of 4; of 5.

3. Find the fourth power of 1; of 2; of 3.

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4. 102, 103, 104, 105, are read "ten square," "ten cube," "ten fourth power," and "ten fifth power," respectively. Tell the meaning and value of each indicated power.

5. Multiply by 3, or square 3.

6. Square; ; ; ; .3; .5; .7; .12; 1.2.

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7. Cube;;; † ; .2; .3; .5; .1; .02; .05.

519. The square of a fraction may be obtained by squaring both terms; the cube, by cubing both terms; etc.

WRITTEN EXERCISES

520. Raise each of the following to the power indicated:

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Find the volume of a cube whose edge is :

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32. The number of feet a body will fall, from rest, in any number of seconds is 16.08 times the square of the number of seconds. How far will a body fall in 4 sec.? in 15 sec. ?

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