Imágenes de páginas
PDF
EPUB

CHAPTER IX.

Barter; and Profit and Loss.

BARTER.

158. Barter is the exchanging of one commodity for another; value for value, according to rates or prices agreed upon by the parties concerned.

159. RULE.*--Find the value of that commodity whose quantity is given; then find what quantity of the other, at the rate proposed, you may have for the same money, and it gives the answer required.

Example. How much coffee at 164 cents per lb. must be given in barter for 1 pipe of wine, at $1.371 per gallon? Here the price As 1 gal.: 126 gal. :: $1:37: $173.25. of the wine is found by the first

cts. cts. lb. lbs.

As 161: 17325 : : 1 : 1050. analogy to be $173.25, and the number of pounds of coffee is found, by the second analogy, to be 1050 lbs., so that 1 pipe of wine, containing 126 gallons, at $1.37, is equal in value to 1050 lbs. of coffee, at 16 cents per lb.

Exercises.-1. How many yards of linen, at 87 cents per yard, must be given in barter for 6 pieces of black cloth, each containing 37yds. 2qrs. at $5.75 per yard?

Ans. 1478yds. 2qrs. 1n. 2. A. delivered 5 pipes of brandy, at $1.183 per gallon, to B. for 2497 gallons of rye whiskey; what was the whiskey per gallon? Ans. 29cts. 9m.+. 3. How much wheat, at $1.121 per bushel, must be given in barter for 125 barrels of flour, at $5.75 per barrel? Ans. 638 bush.

4. How much barley, at 624 cents per bushel, must be given in barter for 12 barrels of beer, at $6.25 per barrel ? Ans. 120 bush.

5. A. and B. barter; A. has 25 barrels of cider, at $4.50 per barrel, for which B. gave him 76 lbs. of tea, at 94 cents

This rule is, evidently, only an application of the rule of Simple Proportion.

Ib. ;

how

per lb. and the rest in sugar, at 10 cents per much sugar must B. give A. besides the tea? Ans. 4831§lbs. 6. A. bas 3 hhds. of sugar, weight neat 27cwt. 3qrs. 14lbs. at $9.50 per cwt., for which he receives from B. in barter, 2 chests of tea, each containing 95 lbs. at $1.09 per lb. and the rest in money; how much money did Ă. receive from B. ? Ans. $56.833.

Profit and Loss.

160. That branch of Arithmetic which treats of the gains or losses on mercantile transactions, is called profit and loss; and it teaches merchants how to fix the price of their goods so as to gain so much per cent.*

Questions in this rule are performed by simple proportion, upon this principle, that quantities, or sums of money, which gain or lose at the same rate, are to one another as their gains or losses. The method of performing the first example and the first six exercises, is so obvious as not to require a formal rule.

Example. If 1 cwt. of sugar be bought for $10.50, and sold at 11 cents per lb. what is the gain?

[blocks in formation]

Exercises.-1. If a piece of cloth, containing 31yds. 2qrs. cost $187, what is gained by selling it at $7.25 per yard? Ans. $40.87% 2. Bought 212cwt. 1qr. 14lb. of pork, at $4.25 per cwt. and the charges amount to $75.75; what is the gain or loss, Ans. Gain $507.274. gallons, cost $250.50, per gallon?

by selling it at 61 cents per lb. ?

3. If a pipe of wine, containing 130 what is gained by selling it at $2.12

Ans. $25-75.

* It should be particularly remarked, that by the gain or loss per cent. is to be understood the sum that would be gained or lost at the given rates, not on a hundred dollars worth sold, but on a hundred dollars laid out in prime cost, and in charges, if there be any.

4. If a chest of tea, containing 110 lbs. be sold at $1.13 per lb,, what is the gain, the first cost being $96.75?

Ans. $27.55.

5. If a cwt. of pork be bought for $6.25, and sold at 61 cents per lb., what is the gain? Ans. $0.75. 6. If a barrel of cider, containing 31 gallons, be bought for $4.25, what is gained by selling it at 61 cents a pint? Ans. $11.50,

PROBLEM I.-From the prime cost and selling price, to find the gain or loss per cent.

161. RULE. As the prime cost to the gain or loss on the cost: $100: the gain or loss per cent.

Exam. 2. If tea be bought at 872 cents per lb. and sold at $1.124 per lb., what is the gain per cent. ?

From $1:21

Take

-87

As 87 cts. 25 cts.: $100:

Here, $1.12-87-25 cents, the gain on 87 cents; then, as 87 cents (the first cost of 1 lb.): 25 cents, (the gain on 87 cents): $100 (regard as first cost): $28.574, the gain per cent., or the gain on $100.

Exam. 3. If coffee be bought at 163 cents per lb., and sold at 16 cents per lb., what is the loss per cent. ?

Here, subtracting 16 from 162, the remainder iscent, which is the loss on 163 cents; therefore, as 163::: $100 $1.491, nearly, the loss per cent., or the loss on 100 dollars.

Ex.-7. If wine, which cost $1.372 per gallon, be sold for $1.62, what is gained per cent.? Ans. $18.18.1. 8. If paper, which cost $4.25 per ream, be sold for $3.95 per ream, how much is lost per cent.? Ans.$7.05.814 9. If sugar cost $9.374 per cwt., and sold at 112 cents per lb., what is gained per cent.? Ans. $37.3818.

10. Bought tea at 94 cents per lb., and sold it at $1.10 per lb., how much is the gain per cent. ? Ans. $17·02 113. 11. Bought Newton's Principia for $10.80, and sold it for $10, how much is the loss per cent.? Ans. $7 40-74. 12. Bought Gregory's Mechanics for $11.50, and sold it for $14, how much is the gain per cent.? Ans.$21.73.933. 13. Bought Wheewell's Mechanics and Dynamics for $7.25, Laplace's System of the World for $5.75, Bonnycastle's Algebra for $6.371⁄2, and Simpson's Fluxions for $5.75 :

sold all those books for $30; how much is the gain per cent. ? Ans. $19.4039

[ocr errors]

PROBLEM II. To find how a commodity must be sold to gain or lose a certain rate per cent.

162. RULE-As $100 the gain or loss per cent. :: the prime cost: the gain or loss on that cost; and from this and the prime cost, the selling price will be found by addition or subtraction.

Exam. 4. How must tea, which cost 92 cents per lb. be sold to gain 25 per cent. ?

Here, as $100 (regarded as first cost): 325 (the gain on $100) :: 92 cents (the first cost of 1 lb.): 23 cents,

As $100 $25: 92 cents :

[merged small][ocr errors][merged small][merged small][merged small]

the gain per lb. which being added to 92 cents, the amount is $1.15, the required rate.

5. Sold a pipe of wine, which cost $1.75 per gallon, at a loss of 121 per cent.; at what rate per gallon was it sold? Here, the loss on As $100: $12 $1.75: 217 cts. From $1.75 cost

$1.75, is found to be 217 cents, which, taken from $1.75, the first cost, gives the rate required.

Take •217 loss

$1.531 sales.

Ex. 14. How must wine, which cost $1.27 per gallon, be sold to gain 20 per cent.?

Ans. $1.52.4.

15. How must linen, which cost 56 cents per yard, be

sold to gain 30 per cent. ?

Ans. $0.72.8. 16. How must superfine black cloth, which cost $9.75 per yard, be sold to gain 22 per cent. ? Ans. $11.891. 17. Sold a piece of linen, which cost 75 cents per yard, at a loss of 20 per cent., at what rate per yard was it sold ? Ans. $0.60.

18. Bought a book for $14.50, and sold it at a loss of 121 per cent. For how much was the book sold? Ans. $12 683. 19. How must pork, which cost 4 cents per lb., be sold

to gain 20 per cent. ?

20. Bought beef at 32 cents per lb. to gain 37 per cent.?

Ans. $0.05.4.

How must I sell it
Ans. $0.05-1.

PROBLEM III.--From the gain per cent, and the selling price, to find the first cost.

163. RULE.-As $100, together with the gain per cent., or diminished by the loss per cent.: $100: the selling price to the prime cost.

Exam. 6. What was the first cost of brandy, which being sold at $1.15 per gallon, the seller clears 20 per cent.? In this example, it is evi- As $120 $100 $1.15 dent, that what cost $100 is sold for $120; and the analogy is no more than this: as the selling price, $120, is to its first cost, $100, so is the selling price, $1.15, to

its corresponding first cost, 955 cents.

6

5

5

6)5.75

Ans. 95 cts.

Exam. 7. If a merchant, by selling wine at $2.25 per gallon, lose 18 per cent., what was the prime cost?

As $82 (-100-18): $100 $2.25: $2.741.

In this example, it is evident, that what cost $100 must have been sold for $82; and therefore the preceding analogy is simply this as the selling price, $82, is to the corresponding first cost, $100, so is the selling price, $2.25, to the corresponding first cost, $2.741, or $2.75, nearly.

Fx. 21. If 12 per cent. be lost by selling 128 yards of broadcloth for $500, what was the prime cost per yard? Ans. $568

22. Suppose a book to be sold for $35.50, and 20 per cent. to be gained, what was the prime cost? Ans. $29.58. 23. If 15 per cent. be gained by selling tea at $1.12 per lb., what was the first cost, and what was gained by the sale of 350 lbs. ? Ans. 971 cents first cost, $51-36 gain. Exam. 8. If 20 per cent. be gained by selling wine at $2.12 per gallon, how must it be sold to gain 25 per

cent.?

:

This example might be wrought by finding the first cost, and thence the selling prices, as in the preceding exercises. It will be wrought more easily, however, by this analogy; as $120 $125 $2-12: the price required. The reason of this will be manifest, if it be considered, that what cost $100, in the one case sold for $120, and in the other for $125; and therefore, the above analogy is no more than this as the selling price of one hundred dollars worth in T

« AnteriorContinuar »