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1. A. and B. engage in trade. A. furnishes $300, and B. $400 of the capital. They gain $182. What is each one's share of the gain?

2. Two persons form a partnership. A. puts in $450 for 7 mo. and B. $300 for 9 mo. They lose $156. How much is each man's share of the loss?

3. A., B., and C. paid $220.50 for a pasture. A. put in 9 cows for 2 mo., B. 12 cows for 2 mo., C. 18 cows for 1 How much of the rent ought each to pay?

mo.

4. C., D., and E. formed a partnership for carrying on business. C. furnished $800 for 6 mo., D. $1800 for 8 mo., and E. $1500 for 4 mo. They gained $940. How should the gain be divided?

A. put in What was each

5. A., B., C., and D. traded in company. $7500, B. $7000, C. $9500, and D. $8000. partner's share of a profit amounting to $9280?

6. Three men buy a house for $1200. A. furnishes $600, B. $400, C. $200. They sell the house for $1500. How much money should each receive?

7. M. and N. entered into partnership. M. put $200 into the business for 5 mo. and N. $300 for 4 mo. They gained $132. Find the share of each?

8. Two men hire a pasture for $42. One puts in twice as many head of cattle as the other. What should each pay?

9. A., B., and C. buy a house for $15,000. A. supplies $4000, B. $5000, C. the remainder. The yearly rental being $1000, to what part of it is each entitled?

10. E., F., and G. bought a block of stores for $46,000. E. furnished of the money, F. $11,500, and G. the rest. The property was sold for $48,300. What was the gain of each?

11. A., B., and C. engaged in manufacturing. A. invested $4500 for 6 mo., B. $5000 for 8 mo., and C. $6500 for 7 mo. They gained $4500. Find each partner's gain.

12. The profits were $4800. Patterson's share was $3000. How many eighths of the capital did he own?

13. X. and Y. hire a bicycle for $4.50 a week. If X. uses it on Tuesday and Friday, and Y. the rest of the week, except Sunday, what does each pay?

14. Smith and Jones united in a partnership. Smith contributed $240 for 8 mo., and B. $560 for 5 mo. They lost $118. How much did each man lose?

15. A man dies owing three creditors, $8050, $2970, and $7170, respectively. If his assets, after deducting expenses, are $13,646, how much will each creditor receive?

16. A. and B. enter into partnership with capitals of $3500 and $8700. A. is to have 12% of the profits for his services as manager. Divide a gross profit of $1906.25.

17. S. and T. engaged in speculation. S. employed $1260 for 8 mo., and T. $980 for 6 mo. They lost $957.60. Apportion this loss.

18. A man failing in business, paid 50 cents on the dollar. With assets of $40,000, how much would X., Y., and Z. receive, whose claims against him were respectively $2000, $3000, and $4000?

19. Apportion a loss of $5600 among three partners whose capital was invested in the proportion of 1, 4, and 5.

20. A. commenced business January 1st, with a capital of $3400. April 1st he took B. into partnership with a capital of $2600; at the expiration of the year, they had gained $750. What is each one's share of the gain?

21. Our standard gold coin consists of 900 parts of gold, 90 parts silver, 10 parts copper. What is the quantity of each metal in 50 pounds of coin?

22. A. and B., contractors, received $857.50 for grading a roadway. A. furnished 5 men 20 days, and 6 others for 15 days; B. furnished 10 men for 12 days, and 9 others for 20 days. What was each contractor's share?

23. C. and D. form a partnership. C. invests $5000; D. $10,000. During the year C. draws $1500 of the profits and D. draws $1000. At the end of the year the business is disposed of for $20,000. What amount should each receive?

24. P., Q., and R. buy a lot for $600. After selling it, P. receives $220 as his share of the proceeds, Q. receives $280 and R. $300. How much did each invest originally?

25. A partnership is formed between A., with a capital of $1500, and B., with a capital of $4000. Six months thereafter they take in C., with a capital of $4000. How should a profit of $3500 be divided at the end of the year?

26. V. and W. rented a field for a year for $200. V. put in 6 horses for the whole time, W. put in 5 horses for 11 months and 3 horses for 5 months. How much of the rent had each to pay?

27. A., B., and C. entered into partnership for one year. A. put in $5000, B. $6000, and C. $4000. At the end of six months A. withdrew $2000, and C. put in $8000 more. The profits at the end of the year were $6000. What was each man's share?

28. B. and C., trading together, find their stock to be worth $3500, of which C. owns $2100. They have gained 40% on their first capital. What did each put in?

AVERAGES.

An average is expressed by the ratio of the sum of two or more quantities to the number of the quantities.

ILLUSTRATION.

A Fahrenheit thermometer registered 30° at 8 A.M., 56° at M., and 40° at 6 P.M. What was the average temperature of the day between 8 and 6 o'clock?

Process.

1. The sum of the quantities is 30 + 56 + 40 = 126. 2. The number of them is 3.

3. Their average is 136

= 42.

Therefore the average temperature is 42°.

PROBLEMS.

1. A tax-collector received on Monday, $430.74; on Tuesday, $380.88; on Wednesday, $448.60; on Thursday, $420.79; on Friday, $367.44; on Saturday, $508.73. What did he receive daily on an average?

2. In a school the largest attendance present for each of six months was as follows: 1st mo., 125; 2d mo., 130; 3d mo., 128; 4th mo., 125; 5th mo., 132; 6th mo., 122. Find the average attendance for the 6 months.

3. A goldsmith combined 2 oz. of gold 16 carats fine, 2 oz. 18 carats fine, and 6 oz. 22 carats fine. What is the fineness

of the composition?

4. If one dozen eggs weigh 1 lb. 2 oz., what is their average weight?

5. If a man owes a debt, due in 3 mo., and a like debt, due in 5 mo., when may he pay both debts at once?

AVERAGING OR EQUATING OF PAYMENTS.

The averaging or equating of payments due at different times consists in finding an equitable time for including all payments in one.

ILLUSTRATION.

A. owes B. $250, due in 3 mo., and $350, due in 5 mo. Find the average term of credit?

NOTE. If the payments were equal, the average term of credit would be 5+3 = 4 mo. Since they are not equal, we must consider both time and

2

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1. Multiply the debts by the terms of credit.

2. Divide the sum of the products by the sum of the debts.

PROBLEMS.

1. Equate the time for payment of $400, due in 3 mo.; $600, due in 7 mo. ; and $300, due in 10 mo.

2. Find the average time of payment of $3500, due in 5 mo.; of $1600, due in 8 mo. ; of $1500, due in 10 mo.; and of $600, due in 9 mo.

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