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EQUATION OF PAYMENTS, IS finding the equated time to pay at once, several debts due at different periods of time, so that no loss shall be sustained by either party.
Rule.-Multiply each payment by its time, and divide the sum of the several products by the whole debt, and the quotient will be the equated time for the payment of the whole.
1. A owes B 380 dollars, to be paid as follows-viz. 100 dollars in 6 months, 120 dollars in 7 months, and 160 dol. Jars in 10 months: What is the equated time for the payment of the whole debt ?
100 X 6 600
)3040(8 months. Ans. 2. A merchant hath owing him 3001. to be paid as fol lows : 501. at 2 months, 100l. at 5 months, and the rest at 8 months; and it is agreed to make one payment of the whole: I demand the equated time ? Ans, 6 months.
3. F owes H 1000 dollars, whereof 200 dollars is to be paid present, 400 dollars at 5 months, and the rest at 15 months, but they agree to make one payment of the whole; I demand when that time must be ? Ans. 8 months.
4. A merchant has due to him a certain sum of money, to be paid one sixth at: 2 months, one third at 3 months, and the rest at 6 months ; what is the equated time for the payment of the whole ?
Ans. 4 months.
BARTER, IS the exchanging of one commodity for another, and directs merchants and traders how to make the exchange without loss to either party.
RULE. Find the value of the commodity whose quantity is given; then find what quantity of the other at the proposed rate can be bought for the same money, and it gives the answer.
1. What quantity of flax at 9 cts. per lb. must be given in barter for 12 lb. of indigo, at 2 dols. 19 cents per lb. ?
12 lb. of indigo at 2 dols. 19 cts. per lb. comes to 26 dols. 28 cts.therefore, As 9 cts. : 1 lb. : : 26,28 cts. : 292 the answer.
2. How much wheat at 1 dol. 25 cts. a bushel, must be given in barter for 50 bushels of rye, at 70 cts, a bushel ?
Ans. 28 bushels. 3. How much rice at 28s. per cwt. must be bartered for 3) cwt. of raisins, at 5d.
Ans. 5 cut. 3 qrs. 91 izlo. 4. How much tea at 4s. 9d. per lb. must be given in barter for 78 gallons of brandy, at 12s. 3 d. per gallon ?
Ans. 201 lb. 133 oz. 5. A and B bartered : A had 81 cwt. of sugar at 12 cts. per lb. for which 3 gave him 19 cwt. of flour; what was The flour rated a, per lb.
Ans. 51 cts. 6. B delivered 3 hhds. of brandy, at 6s. 8d. per gallon, to C, for 126 yds. of cloth, what was the cloth per yard ?
Ans. 10s. 7. D gives E 250 yards of druggrt, at 30 cts. per yd. for 319 lbs. of pepper; what does the pepper stand him in
Ans. 23 cts. 516m. 8. A and B bartered: A had 41 cwt. of rice, at 21s. per cwt. for which В gave him 201. in money, and the rest in sugar at 8d. per lb.; I demand how much sugar B gave A besides the 201. ?
Ans. 6 cwt. O qrs. 1971b. 9. Two farmers bartered: A had 120 bushels of wheat at 11 dols. per bushel, for which В gave him 100 bushels of barley, worth 65 cts. per bushel, and the balance in oats at 40 cts. per bushel; what quantity of oats did A receive from B?
Ans. 287! bushels. 10. A hath linen cloth worth 20d. an ell ready money ; but in barter he will have 2s. B hath broadcloth worth 14s. 6d. per yard ready money ; at what price ought B to rate his broadcloth in barter, so as to be equivalent to A's bartering price?
Ans. 17s. 4d. 3 qrs:
per lb. ?
11. A and B barter : A hath 145 gallons of brandy at I dol. 20 cts. per gallon ready money, but in barter he will have 1 dol. 35 cts. per gallor : B has linen at 58 cts. 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 to A's brandy?
Ans. Barter price of B's linen is 65 cts. 2m. and he must give A 300 yds. for his brandy.
12. A has 225 yds. of shalloon, at 2s. ready money per yard, which he barters with B at 2s. 5d. per yard, taking indigo at 12s. 6d. per 1b. which is worth but 10s. how much indigo will pay for the shalloon; and who gets the best bargain?
Ans. 43 lb. at barter price will pay for the shalloon, and B has the advantage in barter. Value of A's cloth, at cash price, is
£22 10 Value of 43;lb. of indigo, at 10s. per lb.
15 B gets the best bargain by £0 15
LOSS AND GAIN, IS a rule by which merchants and traders discover their profit or loss in buying and selling their goods : it also instructs them how to rise or fall in the price of their goods, 80 as to gain or lose so much per cent. or otherwise.
Questions in this rule are answered by the Rule of Three.
1. Bought a piece of cloth containing 85 yards, for 191 dols. 25 cts, and sold the same at 2 dols. 81 cts. per yard ; what is the profit upon the whole piece?
Ans. $47, 60 cts. 2. Bought 12! cwt. of rice, at 3 dols. 45 cts. a cwt. and sold it again at 4 cts. a pound; what was the whole gain ?
Ans. $12, 87 cts. 5m. 3. Bought 11 cwt. of sugar, at 6 d. per lb. but could not sell it again for any more than 21. 16s. per cwt.; did I gain or lose by my bargain
? Ans. Lost, £2 11s. 4d. 4. Bought 44 lb. of tea for 61. 12s. and sold it again for 81. 10s. 68. ; what was the profit on each pound?
Ans. 10 d.
5. Bought a bhd. of molasses containing 119 gallons, at 52 cents per gallon; paid for carting the same i dollar 25 cents, and by accident 9 gallons leaked out; at what rate must I sell the remainder per gallon, to gain 13 dollars in the whole ?
Ans. 69 cts. 2 m.t
II. To know what is gained or lost per cent. RULE.-First see what the gain or loss is hy subtraction; then, As the price it cost : is to the gain or loss : : so is 1001. or $100, to the gain or loss per cent.
EXAMPLES. 1. If I buy Irish linen at 2s. per yard, and sell it again at 2s. 8d. per yard; what do I gain per cent. or in laying out 1001. : As : 2s. 8d. : : 100l. : £33 6s. 8d. Ans.
2. If I buy broadcloth at 3 dols. 44 cts. per yard, and sell ft again at 4 dols. 30 cts. per yard : what do I gain per ct. or in laying out 100 dollars ?
$ cts. Sold for 4, 30
* cts. cts. Cost
As 3 44 : 86 : : 100 : 25
Ans. 25 per cent. Gained per yd. 86
3. If I buy a cwt. of cotton for 34 dols. 86 cts. and sell it again at 41į cts. per lb. what do I gain or lose, and what
* cts. I cwt. at 41} cts. per lb. comes to 46,48
Prime cost 34,86
Gained in the gross, $11,61 As 34,86 : 11,62 : : 100 : 33} Ans. 33} per cent. 4. Bought sugar at 8 d. per lb. and sold it again at 41. 17s. per cwt. what did I gain per cent. ?
Ans. £25 19s. 5 d. 5. If I buy 12 hhds. of wine for 2041. and sell the same again at 141. 178. 6d. per hhd. do I gain or lose, and what
Ans. I lose 12 per cent. 6. At 1 d. profit in a shilling, how much per cent. ?
per cent. ?
Ans. £12 10s.
per cent. ?
7. At 25 cts. profit in a dollar, how much per cent. ?
Ans. 25 per cent. Note.-When goods are bought or sold on credit, you must calculate (by discount) the present worth of their price, in order to find your true gain or loss, &c.
1. Bought 164 yards of broadcloth, at 14s. 6d. per yard ready money, and sold the same again for 1541. 10s. on 6 months credit; what did I gain by the whole; allowing discount at 6 per cent. a year ? £. £.
£. As 103 : 100 : : 154 10 : 150 O present worth.
118 18 prime cost.
Gained £31 2 Answer. 2. If I buy cloth at 4 dols. 16 cts. per yard, on eight months credit, and sell it again at 3 dols. 90 cts. per yd. ready money, what do I lose per cent. allowing 6 per cent. discount on the purchase price? Ans. 21 per cent.
III. To know how a commodity must be sold, to gain or lose so much per cent.
Rule.--As 100 : is to the purchase price : : so is 1001. or 100 dollars, with the profit added, or loss subtracted : to the selling price.
EXAMPLES. 1. If I buy Irish linen at 2s. 3d. per yard; how must I sell it per yard to gain 25 per cent. ?
As 100l. : 2s. 3d. : : 1251. to 2s. 9d. 3 qrs. Ans. 2. If I buy rum at 1 dol. 5 cts. per gallon; how must I sell it per gallon to gain 30 per cent. ?
As $100 : $1,05 : : $130 : $1,361 cts. Ans. 3. If tea cost 54 cts. per lb. ; how must it be sold per lb to lose 12 per cent. ?
As $100 : 54 cts. : : $87, 50 cts. : 47 cts. 2, m. Ans. 4. Bought cloth at 17s. 6d. per yard, which not provin: so good as I expected, I am obliged to lose 15 per cent, by it; how must I sell it per yard? Ans. 14s. 10.d.