2. If $240 gain $21 interest in 15 mo., what will $480 gain

2d C.

240

30

1st C.,

15

21

1st E.

x= $84.

EXPLANATION.-In this example, the causes form a compound ratio, and the required term is an extreme. Hence, the product of the means divided by the product of the given extremes, gives the required term, $84, PRIN. III.

3. If 6 compositors in 14 hr. can set 36 pages of 56 lines each, how many compositors in 12 hr. can set 48 pages of

1st E.,

1st C.

56 14

x=

9 comp.

EXPLANATION. - In this example, the causes and effects each form a compound ratio, and an element of the second cause is required; and the statement is, 6 compositors 14 hours is to a compositors 12 hours as 36 pages of 56 lines each is to 48 pages of 54 lines each. Now, since the required term is an element of one of the means, we divide the continued product of all the elements of the extremes by the PRIN. II. continued product of all the given elements of the means.

4. If 4 horses consume 24 bushels of oats in 12 days, how many bushels will 20 horses consume in 8 weeks?

5. If 10 men can cut 46 cords of wood in 18 da., working 10 hr. a day, how many cords can 40 men cut in 24 da., working 9 hr. a day?

6. If by selling $5000 worth of dry goods, a merchant gains $456.25, what amount must he sell to gain $1000 ?

After the statement of problems by cause and effect, the required term may be obtained as in the first method, by PRIN. II and III.

But by the use of the vertical line and cancellation, a method greatly to be preferred for its simplicity and brevity, the statement of a problem in the form of a proportion may be omitted by observing the following:

Since x represents the required quantity, and may be either a cause or an effect, or an element of the one or of the other, we have this

RULE.-1. Write x alone or with its kindred elements, if it has any, first and ALWAYS on the LEFT of a vertical line, and its corresponding cause or effect on the RIGHT. (74, NOTE 2.)

2. Next, write the other cause and effect, each on the opposite side of the line from that on which the first cause and effect are written.

3. Cancelling equal factors on opposite sides of the line, the product of the remaining factors on the right, divided by the remaining factor or product of the factors on the left, will give the required term.

If any of the terms contain mixed numbers, they should first be changed to improper fractions, or the fractional part to a decimal.

Solve, by either method, the following:

7. If 8 yards of cloth cost $33, how many yards can be bought for $50?

8. What will 87.5 yd. of cloth cost, if 13 yd. cost $1.26? 9. If 1 lb. 4 oz. 10 pwt. of gold may be bought for $260.70, how much may be bought for $39.50?

10. If 5 men reap 52.2 acres in 6 days, how many men will reap 417.6 acres in 12 days?

how

11. If it cost $95.60 to carpet a room 24 ft. by 18 ft., much will it cost to carpet a room 38 ft. by 22 ft. with the same material?

12. What sum of money will produce $300 in 8 mo., if $800 produce $70 in 15 months?

13. How many days will 21 men require to dig a ditch 80 ft. long, 3 ft. wide, and 8 ft. deep, if 7 men can dig a ditch 60 ft. long, 8 ft. wide, and 6 ft. deep, in 12 days?

14. What will be the cost of paving an open court 60.5 ft. long and 44 ft. wide, if 14.25 sq. yd. cost $341 ?

15. What will be the cost of a pile of wood 80 ft. long, 4 ft. wide, 4 ft. high, if a pile 18 ft. long, 4 ft. wide, 6 ft. high cost $30.24 ?

16. If 36 bu. of wheat are bought for $44.50, and sold for $53.50, what is gained on 480 bu. at the same rate?

17. If it cost $15 to carry 20 tons 14 miles, what will it cost to carry 400 tons of a mile?

18. How many men will be required to dig a cellar 45 ft. long, 34.6 ft. wide, and 12.3 ft. deep, in 12 da. of 8.2 hr. each, if 6 men can dig a similar one 22.5 ft. long, 17.3 ft. wide, and 10.25 ft. deep, in 3 da. of 10.25 hr. each ?

19. If a bin 8 ft. long, 4 ft. wide, and 24 ft. deep hold 67 bu., how deep must another bin be made, that is 18 ft. long and 3 ft. wide, to hold 450 bu.?

20. How many days will 12 men require to do a piece of work that 95 men can do in 7 days?

21. If of an acre of land cost $60, what will 45 A. cost? 22. If $750 gain $202.50 in 4 yr. 6 mo., what sum will gain $155.52 in 1 yr. 6 mo. ?

23. If it require 1200 yd. of cloth wide to clothe 500 men, how many yards which is wide will clothe 960 men? 3

24. If by traveling 6 hr. a day at the rate of 41⁄2 mi. an hour, a man perform a journey of 540 mi. in 20 da., in how many days, traveling 9 hr. a day at the rate of 4 mi. an hour, will he travel 600 mi.?

25. If 1 lb. 12 oz. of wool make 24 yd. of cloth 6 qr. wide, how many lb. of wool will it take for 150 yd. of cloth 4 qr. wide?

PARTNERSHIP.

379. Partnership is an association of two or more persons under a certain name, for the transaction of business.

The persons associated are called partners, and the association is called a company, firm, or house.

380. The capital is the money or property invested by the partners, called also investment, or joint-stock.

Capital may be money, real estate, personal property, time, labor, or skill.

381. The resources of a firm are the amounts due it, together with the property of all kinds belonging to it; called also assets or effects.

382. The liabilities of a firm are its debts.

The net capital is the excess of the resources over the liabilities. 383. The gains or losses of a firm are apportioned among its members according to the following

PRINCIPLE. The greater the capital and the longer it is invested, the greater is each partner's share of the gains or losses.

384. To apportion gains or losses according to capital invested.

1. A and B engage in trade; A furnishes $500, and B $700 as capital; they gain $96; what is each man's share?

1200

EXPLANATION.-Since $500, A's capital, is 20% or 5 of the whole capiof the gain, or $40. For a similar reason, B's

tal, he is entitled to

share is of the gain, or $56.

2. Three men engage in trade; A puts in $6470, B $3780, and C $9860, and they gain $7890. What is each partner's share of the profit?

SOLUTION BY PROPORTION.

$6470

$2538.45, A's gain;

$20110: $3780 = :
$7890 $1483.05, B's gain;

The ratio of the whole capital invested to each partner's share of the same, is equal to the ratio of the whole gain or loss to each partner's share of the gain or loss.

We may also regard the whole capital as the first cause, and each man's share of the capital as the second cause, the whole profit or loss as the first effect, and each man's share of the profit or loss as the second effect, and solve by proportion, thus:

$20110: $6470 = $7890: $x = $2538.45, A's gain, etc.

3. Three men trade in company; A furnishes $8000, B $12000, and C $20000 of the capital; their gain is $1680. What is each man's share?

4. Three persons purchased a house for $2800, of which A paid $1200, B $1000, and C $600; they rented it for $224 a year. What part of the rent should each receive?

5. A man failed in business for $20000, and his available means amounted to only $13654. What will two of his creditors respectively receive, to one of whom he owes $3060, and to the other $1530?