A Written Arithmetic, for Common and High Schools

$150, which was

of the whole gain; what was M's gain, and what the sum each invested?

14. Adams & Brown built a schooner. A. furnished $8000, and B. $1700 and 15000 ft. of lumber. Her freights for the first year were $1125, of which B.'s share was $225; what was the price of his lumber per thousand feet?

Ans. $20 per M. partnership. J. puts

15 Jones, Styles & Carpenter enter into in $750, S. $420, and C. 60 tons of coal. They gain $624, of which C. is to have for conducting the business, the balance to be shared among the partners in proportion to their stock in trade. C. receives $390; what is his coal per ton, and what are the shares of the other partners?

For Dictation Exercises, see Key.

COMPOUND PARTNERSHIP.

377. When stock in trade is employed for different periods of time, the partnership is called Compound Partnership.

ILL. EX. Three persons formed a partnership. A put in $170 for 9 mo., B $130 for 12 mo., and C $150 for 8 mo. They gained $286; what was the share of each?

OPERATION.

4290

The use of $170 170 × 9=1530 1530 × $286=$102, A's share. for 9 mo.—the use 130 X 121560 1560 X $286 $104, B's share. of $1530 for 1 mo.; 150 X 8 1200 1200 X $286 $80, C's share. the use of $130 for

4290

12 mo. $1560 for 1 mo.; the use of $150 for 8 mo. $1200 for 1 mo. The amount in trade was, therefore, equal to $1530 + $1560+ $1200, $4290, for 1 mo.; hence the gains should be as follows: A's, 1530 1530 of $286== $102; B's, 18 of $286-$104; C's, 1308 of $286 $80. Hence the

1200

4290

RULE FOR COMPOUND PARTNERSHIP. Multiply each partner's stock by the time it is in trade, and apportion the gain or loss according to the products.

EXAMPLES.

1. A and B engaged in business, and gained $2008.25. A put in $4500 for 9 months, and B $5690 for 7 months. What was the gain of each? Ans. A, $1012.50; B, $995.75.

2. A, B, C, and D work a mine in company. A furnishes $1400 for 3 years, B $500 for 5 years, C $1800 for 2 years, and D $700 for 4 years. At the end of 5 years they divide $2620 of profits; what is the share of each?

Ans. A, $840; B, $500; C, $720; D, $560.

3. Webb, Clapp, and Calhoun form a partnership. Webb puts in $8500 for 7 months, Clapp $10000 for 4 months, and Calhoun $6750 for 9 months. They lose $2499.90. What is each partner's loss?

Ans. Webb, $928.20; Clapp, $624; Calhoun, $947.70. 4. Hooker, Brown, and Lear traded in company. H. put i $2500 for 10 months, B. $2300 for 11 months, and Lear conducts the business, which is considered equal to $2000 in trade, for 12 months. They gain $1486. What should each receive? Ans. Hooker, $500; Brown, $506; Lear, $480.

5. Four persons, J, K, L, and M, loaned money as follows: J $1500 for 5 years, K $750 for 3 years, L $1700 for 24 years, and M $950 for 4 years. They received of interest money $1246. What was the share of each, and what the rate per cent.?

Ans. J, $525; K, $1571; L, $297; M, $266; rate, 7%. 6. A, B, and C formed a copartnership. A furnished & of the capital for 6 months, B of the capital for 10 months, and C the balance for 12 months. The whole gain was $1560. the share of each?

What was

Ans. A, $480; B, $600; C, $480.

7. Hooker & Brown were in business together for 3 years, and gained $5750. Hooker put in $2000 for the first year, and $1500 for the other two; Brown put in $2500 for the first two years, and $1500 for the last year. What was the gain of each?

Ans. Hooker, $2500; Brown, $3250.

8. A and B received $857.50 for grading a road. A furnished 5 hands for 20 days, and 6 others for 15 days; B furnished 10 hands for 12 days, and 9 others for 20 days. What was the share of each contractor? Ans. A, $332.50; B, $525.

9. Lincoln and Hurd hired a pasture, for which they paid $117. Lincoln put in 217 head of cattle for 20 days, 150 for 5 days, 189 for 10 days, and 500 for 7 days; Hurd put in 650 head for 6 days, 48 for 15 days, and 400 for 11 days. What should each pay? Ans. Lincoln, $62.88; Hurd, $54.12. 10. Jones and Avery engaged in business as brokers for the year 1862. Jan. 1, Jones advanced $3600 and Avery $1250; April 1, Tyler was admitted to the firm with $1500; June 1, Childs was admitted with $1200; Sept. 1, Hewins with $1800; and, Nov. 1, Jenkins with $2550. The losses for the year were $7560; what was the loss of each partner?

Ans. Jones, $3534; Avery, $1227; Tyler, $1104; Childs, $687; Hewins, $589; Jenkins, $417. 11. Wallis and Winn engaged in trade. The former had in $900 from January 1 till April 1, when he withdrew $450; July 1 he added $600. The latter had in $2000 from Feb. 1 to Oct. 1, when he added $200; Nov. 1 he withdrew $800. The whole gain during the year was $2500; what was the share of each. Ans. Wallis, $825,7%; Winn, $167418. 12* Ames & Rice ran a steamer for 3 years. Ames furnished $3000 for the first 10 months, when he added $1000 more, and at the end of the second year $500 more. Rice put in $2500 for the first 18 months, when he put in $3500 more. At the end of the third year they found their loss to be $5565; what should each sustain ?

13. D, E, and F hired a pasture on the 20th of May for 5 months, paying $125 for its use. On that day D put in 200 sheep, E 150, and F 80; June 20, D put in 40, E 200, and F 275; July 20, D took out 100, E 75, and F put in 80; Sept. 20, D put in 25, and E and F took out 200 each. What should each pay?

14. Weeks, Wyman & Wentworth engaged in business for 1 year. Jan. 1, each put in $4000; March 1, Weeks and Wyman put in $1500 each, and Wentworth withdrew $600; Aug. 1, Weeks put in $800, Wyman withdrew $300, and Wentworth put in $1000; Oct. 1, Weeks withdrew $400; Nov. 1, Wyman put in $650, and Wentworth put in $1500. At the end of the year they divided $3500 profits. What was the gain of each?

15. A, B, C, and D put $5700 in trade. A's money was in 8 months, and his gain was $160; B's was in 5 months, and his gain was $200; C's was in 2 months, and his gain was $18); D's was in 6 months, and his gain was $240. What stock did each have in? Ans. A, $600; B, $1200; C, $2700; D, $1200. For Dictation Exercises, see Key.

378. QUESTIONS FOR REVIEW.

RATIO. What is ratio? what is arithmetical ratio? geometrical ratio? What is the first term of a ratio called? the second term? both terms when taken together? What is a ratio of equality? of greater inequality? of less inequality? Give an example. In what respect do ratios resemble fractions? How, then, may ratios, at any time, be written? How do you multiply a ratio? how divide a ratio? Suppose you multiply or divide both terms by the same number? What is a simple ratio? a complex? a compound ratio? How do you rcduce a complex ratio to a simple one? a compound ratio? Write a simple ratio; a complex ratio; a compound ratio.

PROPORTION.

- What is proportion? Explain the proportion 2: 4 7:14. What are the 1st and 4th, terms called? the 2d and 3d ? the 1st and 3d? the 2d and 4th? the 1st and 2d? What is inverse proportion? compound proportion? What is a mean proportional between two numbers? Upon what important principle does the solv ing of examples by proportion depend? Write a proportion, and illustrate that principle. How can you find an extreme, when the other three terms are given? how a mean? how a mean proportional between two given numbers? Give the rule for solving an example by simple proportion, and illustrate it by an example of your own. Perform the same example by analysis. What is meant by analysis? Give your rule for solving an example by compound proportion, and illustrate it. In solving any example by proportion, the two terms of a ratio must be of the same kind; why?

Who are the partners?
What is simple partner-

PARTNERSHIP. What is partnership? How are profits and losses usually shared ? ship? (Ans. It is partnership where persons enter into business for the same time.) How do you find each person's share of gain or loss in simple partnership? What is compound partnership? How do you find the shares of gain or loss in compound partnership? Why is partnership sometimes called partitive proportion?

INVOLUTION.

379. Involution consists in raising a number to a required power. (Art. 89.)

380. The required power is indicated by a small figure called the index or exponent, placed at the right, and a little above the number. (Art. 90.)

381. The first power of a number is the number itself. The second power or square of a number is obtained by using the number as a factor twice. The third power or the cube results from using the number as a factor three times, and so on.

NOTE. The most important applications of Involution are in the use of the second and third powers.

382. Any power may be obtained by the following RULE. Employ the given number as a factor as many times as there are units in the exponent of the required power.

EXAMPLES.

1. Find the squares of the integers from 1 to 25 inclusive, and commit them to memory.*