3. A gentleman has due him D600 to be paid as follows, D400 in 10 months, and D200 in 6 months; what is the equated time? Ans. 83 months. 4. A. has due him a certain sum of money to be paid, in 2 months, in 3 months, and the remainder in 6 months; what is the equated time? Ans. 4 months. 5. What is the equated time for paying D2000, of which D500 is due in 3 months, D360 in 5 months, D600 in 8 months, and the balance in 9 months? Ans. 6 months (nearly). 6. What is the equated time for paying D380; whereof D100 is payable in 180 days, D120 in 210 days, D160 in 300 days? Thus, 100 x 180-18000: 120x210=25200 : 160×300= 48000-91200 dividend÷380-240 days, Ans.

RULE II.

See by rule 1, at what time the first man mentioned, ought to pay in his whole money; then, as his money is to his time, so is the other's money to his time; inversely, which, when found, must be added to, or subtracted from, the time at which the second ought to have paid in his money, as the case may require, and the sum, or remainder, will be the true time of the second payment.

7. P. is indebted to Q. D150, to be paid, D50 at 4 months, and D100 at 8 months; Q. owes P. D250, to be paid at 10 months; it is agreed between them that P. make present payment of his whole debt, and that Q. shall pay his so much sooner, as to balance that favor; I demand the time at which Q. must pay the D250.

Thus, 50×4=200; 100 × 8-800-1000÷150=63 months, P.'s equated time; then, D150: 63 months :: D250 : 4 months; then 10 months-4-6 months, time of Q.'s payment. Ans.

Note. Notwithstanding the general use of the rules of equation, they are manifestly incorrect. It is argued by those who defend the principle, that what is gained by keeping some of the debts after they are due, is lost by paying others before they are due; but this can not be the case, for though by keeping a debt after it is due, there is gained the interest of it for that time, yet by paying a debt before it is due, the payer does not lose the interest for that time, but the discount only, which is less than the interest; consequently, the rule can not be strictly correct; although in most questions which occur in business the error is so trifling that it will always be made use of as the most eligible method. The same system of erroneous calculation in regard

to interest and discount is exhibited in equation, by a misapplication of terms, and a false principle.

Note 2.-Suppose a sum of money be due immediately, and another at the expiration of a certain given time forward, and it is proposed to find a time, so that neither party shall sustain loss; now, it is plain that the equated time must fall between the two payments, and that what is gained by keeping the first debt after is due, should be equal to what is lost by paying the second debt before it is due; but the gain arising from the keeping of a sum of money after it is due, is evidently equal to the interest of the debt for that time; and the loss which is sustained by the paying of a sum of money before it is due, is evidently the discount of the debt for that time; therefore it is obvious that the debtor must retain the sum immediately due, or the first payment, till its interest shall be equal to the discount of the second sum for the time it is paid before due; because in that case the gain and loss will be equal, and consequently neither party can be a loser.

REVIEW.

For what purpose is equation used? What is the first rule? The second? What can you say in relation to the correctness of the principle of calculating equations of time of payment?

BARTER.

THIS is a rule by which merchants and others exchange one commodity for another, and by which they know how to make the exchange, or proportion the quantities without loss to either. party; the rules in Barter, Profit and Loss, and Partnership, are only applications of the rules of proportion which have been explained and are easily understood.

RULE I.

Find the value of what you propose to exchange at the price at which you wish to exchange it, by any rule most convenient. Then, as the price of one of the articles which you receive, is to the whole quantity, so is the whole value of what you give in exchange, to the answer required.

QUESTIONS.

1. A. has 200 pounds of tea at D1.25 per pound, which he will let B. have in exchange for sugar at 11c. per pound; how much sugar must A. receive for his tea?

Thus D1.25 per lb. tea.

Or, as 11c.

200 lb. tea.

c.11)250.00(2272lb. 11oz.+ Ans.
200lb. :: D1.25

2272lb. 11oz.

2. A. and B. barter, A. sold B. 4.5 yards of broadcloth at D5.25 per yard, 150 lb. of pork at 8.5 per lb., and one barrel of mackerel at D10.25; B. let A. have 2.5 cords of wood at D3.75 per cord, 10 bushels of wheat at D1.25 per bushel, and 7 bushels of rye at 80c. per bushel; how does the account stand? Ans. B. must pay to A. D19.15.

3. D. sold a horse for D75, one half was paid in cash down and the remainder in oats at 37.5c. per bushel; bushels of oats did he receive?

how many

Ans. 100.

4. How much corn at 87.5c. per bushel, is equal to 464 bushels of wheat at D1.25 per bushel?

Ans. 662 bushels, 3 pecks, 3 quarts. 5. How much tallow at 8.5c. will you receive in barter, for 12cwt. 2qrs. 8lb. of sugar at 15c. per lb. ? Ans. 2484lb. 11oz. 6. C. has 2 pieces of broadcloth; 1 piece contains 30 yards at D4.50 per yard; the other 25 yards at D3.75 per yard, which he will barter with P. for 2000lb. of pork at 10.5c. per lb. and the balance in flax at 12c. per lb.; how much flax will C. receive? Ans. 150lb.

7. W. has 3 hogsheads of wine at D1.12 per gallon, for the value of one half he will take wheat, at D1.10 per bushel, and for the remainder he will take 250 yards of domestic cloth; how much wheat will he receive, and how much will the cloth cost him per yard?

Ans. 96 bushels, 6 quarts, 1 pint, wheat; and cost of cloth, c.42.3+ per yard.

8. How much butter at 14c. per pound must be given for 85 pounds of ham at 16c. per pound, and 8 pounds of tea at D1.25 per pound? Ans. 168lb. 9oz.

9. Two farmers bartered; A. had 120 bushels of wheat at D1.50 per bushel, for which B. gave him 100 bushels of barley worth 65c. per bushel, and the balance in oats at 40c. per bushel; what quantity of oats did A. receive? Ans. 287.5 bush.

10. A merchant sold 14.5 yards of broadcloth at D4.25 per yard, and received in payment 95lb. of wool at 31.25c. per lb., 15doz. of eggs at 16c. per dozen, 4.25 bushels of wheat at D1.12 per bushel, a quarter of beef weighing 164lb. at 6c. per lb., 471b. of tallow at 12c. per lb., 8 bushels of rye at 93 c. per bushel;

and 781c. in cash; how much more must he (A) receive for his cloth?

Ans. 0.

11. A. and B. bartered; A. had 8.25 cwt. of sugar at 12 cts. per lb., for which B. gave him 18 cwt. of flour; how much was the flour per lb. ?

Ans. 5.5c.

12. B. has 5 pieces of muslin, each piece containing 95 yards at 23c. per yard, for which C. is to give him 32 sheep at D2.50 each, and the remainder in rye flour at D1.50 per cwt.; how many cwt. of flour must C. receive? Ans. 19cwt. 2qr.

13. A. purchased a flock of sheep of B. consisting of 75 in number, at D1.75 each; he paid B. D87.50 in cash, 1.5 tons of hay at D7.50 per ton, and 9 bushels of corn at 624c. per bushel; required the balance due. Ans. D26.87.5.

Having the ready money and bartering price of one article given and the ready money price and quantity of another article given, to find the bartering price and the quantity of the other.

RULE II.

As the ready money price of the one price of the other so is the bartering the bartering price of the second.

is to the ready money price of the first to

14. A. and B. barter; A. has 145 gallons of wine at D1.20 per gallon ready money, but in barter will have D1.35 per gallon; B. has linen at 58c. per yard, ready money; how must B. sell his linen per yard, in proportion to A.'s bartering price, and how many yards are equal in value to A.'s wine?

Ans. 65.25c. linen per yard, and 300 yards. 15. A. has wheat worth D1.13 per bushel ready money, but in barter he will have D1.33 per bushel; B. has butter worth 20c. per lb. ready money; how must B. rate the butter to be equal to the wheat? Ans. 23.5c. 16. P. has indigo worth D1.00 per pound ready money, but in barter he will have D1.13 per pound; C. has sugar worth 10c. per pound ready money; how must C. rate his sugar that it may be equal with the indigo? Ans. 11.3c.

17. A. has coffee worth 20c. per lb. in ready money, but in barter he will have 25c. per lb.; B has broadcloth worth D2 per yard ready money; at what price ought the broadcloth to be rated in barter? Ans. D2.50.

18. A. has 320 doz. of candles at D1.20 per dozen, for which B. agrees to pay him D160 in cash, and the rest in cotton at 20c. per lb. ; how much cotton must B. give A.?

Ans. 1120lb.

19. A person purchased 120 tons of iron at D10.25 per ton, and paid as follows, namely: In cash D500; 27 bushels of salt at 65c. per bushel; 150lb. of leather at 25c. per lb.; 8 bushels of clover-seed at D4.75 per bushel; 15 bushels of flax-seed at D1.10 per bushel; 75 gallons of currant wine at D1.25 per gallon; 250 bushels of oats at 37.5 per bushel; and he is to pay the balance in honey at 75c. per gallon; required the balance due, and the quantity of honey to be paid.

Ans. Due D432.95; honey 577 gallons, 1 quart. 20. H. has 75 sheep at D1.75 each, for which W. is to give him D109 in cash, and the rest in corn at 62.5c. per bushel; how much corn must W. give H.?

Ans. 35 bushels, 2 pecks, 3 quarts.

21. P. and Q. barter; P. has Irish linen at 60c. per yard, but in barter he will have 64c. per yard; Q. delivers him broadcloth at D6 per yard, worth only D5.50 per yard; which has the advantage in the bargain, and how much linen does P. give Q. for 148 yards of broadcloth?

:

:

As 60 64: 5.50 5.862; therefore, Q. by selling at D6 has the advantage; then 6 148 yards: 64: 15783 yds. Ans. 22. A. has linen cloth at 30c. per yard ready money, in barter 36c., B. has 3610 yards of riband at 22c. per yard ready money, and would have of A. D200 in ready money, and the rest in linen cloth; what rate does the riband bear in barter per yard, and how much linen must A. give B.? The rate of riband is 26.4c. per yard, and B. must receive 1980 yards of linen and D200 in cash.

23. A. has 150 yards of linen, at 25c. per yard, which he wishes to exchange with B. for muslin at 50c. per yard; how much muslin must A. receive? Ans. 75 yards.

24. A. had 200 barrels of flour at D10.50 per barrel, for which B. gave him D1090 in money, and the rest in molasses at 20c. per gallon; how many hogsheads of molasses did he receive? Ans. 80 hogsheads, 10 gallons.

25. A merchant, in bartering with a farmer for wood at D5 per cord, rated his molasses at D25 per hogshead, which was worth no more than D20; what price ought the farmer to have a cord for his wood to be equal to the merchant's bartering price?

Ans. D6.25.

26. A farmer sold a grocer 20 bushels of rye at 75c. per bushel; 200lb. of cheese at 10c. per pound; in exchange for which he received 20 gallons of molasses, at 22c. per gallon, and the balance in money; how much money did he receive? Ans. D30.60