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Equation is a method of reducing several stated times, eat which money is payable, to one mean, or equated time.
RULE. Multiply each payment by its time, add the several products together, and divide the sum by the whole debt; the quotient will be the equated time.
PROOF. The interest of the sum payable at the equated time, at any given rate, will equal the interest of the several payments, for their respective times, at the same rate.
EXAMPLES. 1. C. owes D. 100 dollars, of which 50 dollars is to be paid at 2 months, and 50 at 4 months; but they agree that the whole shall be paid at one time; when must it be paid?
Ans. 3 months. 50 X 2 = 100 50 X 4
2. A. owes B. 380L. of which 100L is to be paid at 6 months, 120L. at 7 months, and 160L. at 10 months ; but they agree that the whole shall be paid at one time: when must it be paid ?
Ans. at 8 months. 3. A merchant has owing to him 300L. to be paid as follows: 50L. at 2 months, 100L. at 5 months, and 150L. at 8 months; it is agreed to make one payment of the whole; at what time must it be paid ? Ans. 6 months.
4. F. owes H. 2400 dollars, of which 480 dollars are to be paid at present, 960 dollars at 5 months, and the rest at 10 months, but they agree to make one payment of the whole, and wish to know the time. Ans. 6 months.
5. A merchant has purchased goods to the amount of 2000 dollars, of which sum 400 dollars are to be paid at present, 800 dollars at 6 months, and the rest at 9 months: but it is agreed to make one payment of the whole; what is the equated time?
Ans. 6 months.
6. G. owes K. 420L, which will be due 6 months hence; it is agreed that 60 L. shall be paid now, and that the rest remain unpaid a longer time than 6 months; when must it be paid ?
Ans. in 7 months
Barter is the exchanging of one commodity for another, according to the price or value agreed upon by the parties concerned.
Questions relating to barter are solved, either by the Rule of Three or by Practice.
Note.-When a given quantity of any commodity at a given price, is to be bartered for another commodity at a given price, find the value, in money, of that commodity whose quantity is given; then find what quantity of the other may be had for that value.
EXAMPLES. 1. How much sugar at 11d. per lb. must be given in barter for 1100lb. of rice at 3 d. per lb. ? Ans. 350 lb. 16.
d. 16. d. 16. 1100
11:1:: 3850 : 350 3
3850 d. the value of the rice: 2. How much sugar at 9d. per lb. must be given in barter for 4921b. of rice, at 3d. per lb.?
Ans. 164 lb. - 3. How much tea at 64 cents per lb. must be given in barter for 448 lb. of coffee at 20 cts. per ib. ? Ans. 140 lb.
4. What quantity of tea at 10s. per lb. must be given for 720 lb. of chocolate, at 45. 2d. per
Ib. ? Ans, 300 lb. 5. How much wheat at i dol. 25 cts. per bushel, is equal in value to 50 bushels of rye, at 70 cents per bushel ?
Ans. 28 busheis. L
6. B. has 75 yards of muslin, at Is. 4d. per yard, which he is to give to H. for linen, at 55. per yard; how much linen will he receive?
Ans. 20 yards. 7. A. has sugar at 9d. per lb. for a quantity of which F. is to give him 225 lb. of tea, at 6s. per lb.; how much sugar must F. réceive for his tea?
Ans. 1800 lb. 8. How much sugar at 8d. per lb, must be given in barter for 20 cwt. of tobacco, at 3L. per cwt. ?
Ans. 16 cwt. O qrs. 8 lb. 9. A merchant has 1000 yards of canvass, at 9 £d. per yard, which he is to barter for serge, at 101d. per yard; how many yards of serge should he receive?
Ans. 9.644 yards. 10. A grocer bartered 5 cwt. of sugar at 6d. per
Ib. for cinnamon at 10s. 8d. per 1b.; how much cinnamon did he receive ?
Ans. 26 lb. 402. 11. A. has 41 cwt. of hops, at 30s. per cwt. for which B. is to give him 20 L. in money, and the rest in prunes at 5d. per Ib. what quantity of prunes must A. receive ?
Ans. 1992 lb. 12. A. and B. barter: A. has 320 lb. of chocolate, at 45. 6d. per lb. for which B. is to give him 30 L. in money, and the rest in cotton at 8d. per Ib. How much cotton is B. to give A.?
Ans. 1260 lb. 13. L. has 41 cwt. of hops, at 4 dols. 50 cts. per cwt. for which M. is to give him 28 dols. 50 cts. in money, and the rest in salt, at 80 cts. per bushel; what quantity of salt is M. to give L. ?
Ans. 195 bushels. 14. G. has 281 lb. of tea, at 11s. 6d. per Ib. for which B. is to give him 40 yards of linen, at 7s. 4d. per yard, and the rest in money; how much money must G. receive?
Ans. IL. 14s. 5d. 15. R. gave 189 yards of linen, at 6s. 8d. per yard, to C, for 42 yards of cloth; what was the cloth per yard?
Ans. 30s. 16. A. has 608 yards of cloth, at 14s. per yard, for which B. is to give him 125L. 12s. in money, and 85 cwt. 2 qrs.
24 lb. of bees-wax. At how much is the bces-wax valucd per cwt.?
Ans. 3L, 10s. 17. C. lias wheat at $1.25 cents per bushel, ready money; but in barter he will have $7.50 per bushel ;
D. has cotton at 20 cents per lb. ready money: what price must the cotton be in barter, and how much must be given for 100 bushels of wheat ?
The cotton must be 24 cts. per lb. and 625 16. Ans.
must be given for 100 bushels of wheat.
LOSS AND GAIN.
Loss and Gain instructs merchants and traders, so to estimate their goods, in buying and selling, as to know what they gain or lose in dealing,
Questions in Loss and Gain are solved by the Rule of Three or by Practice.
EXAMPLES. 1. A storekeeper sold 100 yards of silk, at $1.50 per yard, which cost him $1.25; how much did he gain by the sale ? $1.50
yd. cts. yde. $1.25
1 : 25 : : 100
100 25. gain per yard.
Whole gain $25.00 2. If a grocer buy 265 lb. of tea for 79 L. 10s. and afterwards sell
the whole at 7s. per lb. how much will he gain by the transaction?
L. 265 at 7s,
Sold for 92 15 7
Cost 79. 10
92 L. 15$. 3. A shopkeeper bought 53 yards of silk, at 12s. per yard, and afterward sold it at 14s. per yard; how much did he gain by the sale ?
Ans. 5L. 6s. 4. G. bought 650 lb. of sugar, at 10 cents per lb. and sold it at 12 cents per lb.; how much did he gain ?
5. If I buy 765 yards of baize, at 3s. 41d. per yard, and sell it at 3s. 9d. per yard, how much do I gain?
Ans. 14L. 6s. 1014. 6. Bought 2016 lb. of rice at 3d. per Ib, and sold it at 3 d. per 15.; how much was gained by the transaction?
Ans. 4L. 4s. 7. If I lay out 1000 dollars in hats, at 4 dollars each, and sell them afterward at 4 dols. 50 cts. each, how much will I gain?
Ans. 125 dols. 8. A merchant bought 1300 lb. of coffee, at 22 cts. per Ib. and was afterward obliged to sell it at 20 cts. per lb. how much did he lose ?
Ans. $26.00. 9. B. laid out 250 L. in cloth, at 30s. per yard, and, afterward, finding it was damaged, sold it at 27s. 6d. per yard; how much did he lose?
Ans. 31 L, 5s. 10. A shopkeeper bought 42 yards of muslin for 4L. 145. 8d. and sold it at 2s. 6d. per yard; whether did he gain or lose, and how much? Ans. He gained 10s. 4d.
11 A draper bought 100 yards of cloth for 56 dollars, how must he sell it per yard to gain 19 dollars in the whole?
Ans. 75 cents. 12. If a grocer buy a quantity of tea for 125 L. and sell it again for 150 L. how much will he gain per cent ?
Ans. 20 per cent. 13. If a yard of mantua be purchased for $1.20, and sold again for $1.50, what is the gain per cent ?
Ans. 25 per cent. 14. If a yard of velvet be bought for 16s. and sold again for 12s. what is the loss per cent. ? Ans. 25 per cent.
15. Bought a chest of tea, weighing 490 lb. for 326 dollars, and sold it for $370. 10, what was the profit on each
Ans. 90 cents. 16. If I buy 100 yards of cambrick for 56 L. at how much must I sell it per yard, to gain 15 per cent. ?
Ans. 12s. 103d. 17. Bought 12 pieces of white cloth, for 6 L. 10s. per piece, and paid 20s. 10d. per piece for dying it; how · much must each piece be sold for, to gain 20 per cent?
Ans. 9L. IS, 18. If a trader gain 1 d. per shilling on his goods, how much does he gain per cent.? Ans. 12 per cent.