for the whole to realize a profit of 10 per cent. on the money paid out?

Ans. $543.312.

12. 56. 54. 98. 110

Statement, 12. 6. 100. 100'

12. Bought 700 yards of ribbon, at 6 d. New York currency, per yard; how must I sell the same to gain 12 per cent. and what shall I receive for the whole quantity? Ans. 63 d. per yard, nearly; and for the whole, $49.218.+

13. How must cloth which costs 13 s. 4 d. be sold to gain 20 per cent.? Ans. At 16 s. per yard.

QUESTIONS.-What is profit and loss? What is Case 1st? What is the rule? What is Case 2d? What is the rule? How is the statement made for canceling? What is Case 3d? What is the rule ? What is the rule for canceling?

Ᏼ Ꭺ Ꭱ Ꭲ Ꭼ Ꭱ.

Barter is a rule by which those engaged in trade exchange commodities so that neither party suffer loss.

Take the following illustration:

Ex. 1. How much sugar at 10 d. per lb. must be given in exchange for 12 cwt. of butter at 15 d. per pound?

12. 15

It is obvious that the 12 cwt. of butter bears the same ratio to the number of cwt. of sugar required, as 10 d. bears to 15 d. Therefore, as 10:15::12: the answer, viz. 18 cwt. Or, 10 the statement for canceling:

is

The scholar will perceive that the principle here involved is the same as in the rule of proportion, which has already been fully explained.

2. How much tea at 8 s. per lb. must be given for 2 cwt. of chocolate at 4 s. 6 d. per lb. ? Ans. 1 cwt. 14 lb.

Statement, 8 s. : 4 s. 6 d. : : 2 cwt.: Ans.

In this statement, the price of the chocolate is reduced to The 12 below the line reduces the pence to shillings. pence.

3. How much rice at 32 s. per cwt. must be given for 4 cwt. 2 qr. of raisins at 6 d. per pound? Ans. 7 cwt. 3 qr. 14 lb.

4. B. has 90 yards of linen, worth 4 s. 6 d. per yard, which he wishes to exchange with C. for muslin at 2 s. per yard; how many yards of muslin must B. receive? Ans. 202 yards.

5. Bought 75 yards of broadcloth at $3 per yard, and paid for it in muslin at 1 s. 3 d. New York currency, per yard; how many yards of muslin did it take? Ans. 1440 yards.

6. Bought 7 tuns of wine at 10 d. a pint, and paid for it with melasses at 3 s. per gallon; how many hogsheads of melasses did it take? Ans. 623 hhd.

7. Sold 5 cwt. 1 qr. of sugar at $8.50 per cwt. and received in pay 24 yards of cloth; what was the value of the cloth per yard? Ans. $1.859.

8. How many gallons of melasses at 8 cents a quart must be given for 24 cwt. of rice at $8 per cwt. Ans. 600 gallons. 9. I have nuts worth $4 per bushel, and B. has sugar worth 10 cents per pound; now if I charge him $4.50 per bushel for my nuts, what ought he to charge me for his

114 cents.

sugar ? Ans.

10. What quantity of butter worth 12 cents a pound must be given in exchange for 12 lb. of indigo worth $2.25 per pound? Ans. 216 lb.

11. Sold 5 cwt. of cheese at 8 d. per pound, and received in pay muslin worth 1 s. 6d. per yard; how many yards did I receive? Ans. 2488 yds.

12. Bought 90 bushels of wheat at 15 s. and gave in pay 115 yards of Irish linen, worth 6 s. per yard, and the remainder in cash; how many dollars did I pay, the currency being New York? Ans. $82.50

13. Received of B. a quantity of broadcloth which he had sold at $4.50 per yard, but charged me $5.00; in pay I let him have a quantity of wheat which I had retailed at $1.50 per bushel; what ought I to have charged him, to meet the advance he made on his broadcloth? Ans. $1.66%.

14. Bought 12 gross of pen-knives at 9 dollars per gross, and

paid for them in cloth at 3s. 6 d. New York currency, per yard; how many yards will be required to pay for the knives? Ans. 246 yards.

pay

15. Sold 48 cwt. of hops at 4 d. per pound, and received in prunes at 6 d. per pound; how many cwt. did I receive? Ans. 32 cwt.

16. Received 460 yards of linen worth 6 s. 6 d. New York currency, per yard, in exchange for 84 yd. of broadcloth; what was the value of the broadcloth per yard? Ans. $4.449.+

17. Exchanged 320 lb. of chocolate valued at 4 s. 6d. New York currency, per pound, for a quantity of cotton at 8 d. per lb.; but there not being cotton enough to pay me, I received the balance, viz. 50 dollars, in cash; how many lb. of cotton did I receive? Ans. 1560 lb.

18. How many cwt. of sugar, valued at 10 d. per lb. New England currency, must be given in exchange for 24 cwt. of pepper at 15 dollars per cwt.? Ans. 234 cwt.

19. What deduction ought to be made on wheat, which has been valued at 9 s. per bushel, in exchange for cloth, when cloth valued at 14 s. per yard is sold for 12 s. per yard? Ans. 1 s. 33 d. per bushel.

20. How many pounds of cinnamon at 10 s. per lb. must be given in exchange for 5 cwt. of saleratus at 9 pence per lb. ? Ans. 42 lb.

QUESTIONS.-What is Barter? What is the principle involved in this rule ?

PARTNERSHIP.

Partnership is the rule by which individuals trading with a joint stock, determine their several shares of the profit or loss realized.

The individuals thus trading are called Stockholders. The sum of money advanced by the company forms a Capital Stock; and the money from time to time received on the several shares is called Dividend. When the whole stock owned by the com

pany is employed for the same period of time, the gain or loss which results from the adventure is divided among the individuals composing the company, in proportion to their several shares of the stock.

We have then the following rule:

RULE.—As the whole stock is to each man's share of the stock, so is the whole gain or loss to each man's share of the gain or loss.

Ex. 1. Three persons traded in company. A's stock was $1200; B's stock was $4800, and C's, $2000: they gained $800; what was each man's share of the gain?

$1200+$4800+ $2000=8000, amount of the stock; therefore, 8000: 1200::800: A's share, viz. $120. Then to obtain B's share, 8000: 4800 :: 800: B's share, or $480. And lastly, for C's share, 8000::2000 :: 800: C's share, or $200. To state sums for canceling :

RULE.-Write the whole gain or loss above the horizontal line, with the stock of one of the company standing at the right of it; then place the whole stock below the line, and proceed to cancel, &c.

Note. The operations in this rule are proved by adding together the several shares. Their sum must equal the whole gain. $120+$480+$200-$800.

2. Three men, A., B., and C., traded in company. A. put in $560; B., $700; and C., $640. At the expiration of their partnership, they found that they had gained only $420; what was each man's share? Ans. A's, $123.789; B's, $154.737; and C's, $141.473.

3. Three merchants trading in company suffered a loss of $600; their several stocks were $800, $1000, and $1200; what was each man's loss? Ans. $160, $200, and $240.

4. A., B., and C., freighted a ship. A. put on board 36 tons;

B., 40 tons; and C., 60 tons. In a storm, 30 tons were thrown overboard. What was each man's share of the loss? Ans. A's, 71 tons; B's, 814 tons; and C's, 134 tons.

5. A bankrupt, who has property valued at $2500, owes A. $900; B., 1000; C., $800, and D., $500. How much will each man receive, if the whole property be given up to them? Ans. A., $703.125; B., $781.25; C., $625; and D., $390.625.

6. Three individuals unite in purchasing 600 acres of land. A. pays $3000; B., $5000; and C, $7000. What are their several proportions of the whole? Ans. A. has 120 acres ; B., 200; and C., 280.

7. Three individuals, L., M., and N., freighted a ship with 324 tons burden. L. put on board 72 tons; M., 108 tons; and N., 144 tons. They cleared $1200 by the adventure. What was each man's share of the gain? Ans. L's, $266.666+; M's, $400; and N's, $533.333.+

8. Three persons agreed to pay $150 for the use of a pasture, and that each should pay in proportion to the number of creatures he put in What would be their several shares, provided the first put in 100 oxen; the second, 150 oxen, and the third, 200 oxen? Ans. $33.333+; $50; and $66.666.+

9. A person at his death owes A. 70 £.; E., 400 £.; and H., 140 £.; and his property is valued at only 400 £. How much ought each to receive? Ans. A., 45 £. 182 s.; E., 262 £. 555 s.; and H., 91 £. 16s.

10. Four individuals purchased a horse for $96. A. paid $20; B., $30; C., 25; D., $21. They sold the horse for $150. What was each man's share of the gain? Ans. A's, $11.25; B's, $16.875; C's, $14.064; and D's, $12.814.

11. A man, whose property was worth only $500, owed G., $150; H., $180; and M., $300. He therefore concluded to give his property up to his creditors. What did each receive? Ans. G., $119.047+; H., $142.857; M., $238.095.

12. L. has a farm of 90 acres; M. has one of 120 acres ; and N. one of 150 acres. Their farms all joining, they agree to unite them for the purpose of renting. This they do, and receive for the whole the annual rent of $820; what is each man's share of the rent? Ans. L's, $205; M's, $273.333+; N's, $341.666.+

Whenever the different shares are not continued through the same period of time, it is obvious that each man's share of the profit and loss will depend not entirely on his portion of the