For value received, I promise to pay John P. Smith, or order, Eight Bu red and Seventy-five Dollars, with interest. January 10, 1821. ENDORSEMENTS. Aug. 10, 1824, received $260 HARRY THOMSON $875. Time Dec. 16, 1825, 66 $300 3, 7, 1, 4, 6, 1, 94, July 1, 1827, March 1, 1826, 66 $50 6, 15, 1, 2. What was due September 1, 1828? $150 Ans. $447. $ LXXVI. PRACTICE IN COMPOUND NUMBERS Operations in compound numbers, as pounds, shillings, for instance, may be shortened by taking aliquot parts, as in Practice of Federal Money, ¶ XXVIL 1. What is the cost of 28 bushels of salt, at 10 s. a bushel? In this example, 10s.£.; then, of 28 bushels is the cost in pounds, thus, 28+2= 14£., Ans. 2. What will 40 bushels of wheat cost, at 5 s. = £. a bushel? At 10 s. £.? At 4 s. £.? At 1s.= £.? I. Hence, when the price is an aliquot, or even, part of a pound, we divide the number of gallons, yards, &c. by this aliquot part, as in ¶ XXVIII. Exercises for the Slate. = = = 1. What will 8640 yds. of cloth cost, at 10 s. £. a yd.?4320. At 6 s. 8d.}£.?-2880. At 5 s..?-2160. At 4s.=£. ?-1728. At 3 s. 4 d. £.?-1440. At 2s. 6d. : £.-1080. At 1s. 8d.£. ?-720. At 1 s. 4 d. — =T5£. ?576. At 1s. 3d.£. ?-540. At 1s..?-432. 10 d.==£.?-360. At 8 d. At £.?-288. At 5 d. .-180. At 2 d. £. ?-90. A. 16794£. = Note. The aliquot parts of a pound, in the following examples, may be found in the former examples. 2. What cost 20 gallons of brandy, at 6 s. 8 d. per gallon?~ 6,13,4. 3. What cost 8 yds. of broadcloth, at 10 s. per yard?-4. 4. What cost 25 bushels of rye, at 5 s. per bushel ?-6,5. 5. What cost 30 bushels of oats, at 2 s. 6 d. per bushel ?-3,15, Ans. 20£. 13 s. 4 d. 6. What will 51 bbls. of cider cost, at 7 s. 6d. Ans. 19£. 2s. 6d. = cost, at 7 s. 6d. per bbl. II. Hence, when the price is not an aliquot part of 1£., we may first find what is the greatest even part, and then take parts of this part, and so on, for several times. 7. What will 20 yds. of cloth cost, at 12s. 6d. per yard?-12,10 8. What will 40 yards of cloth cost, at 15 s. per yard ?-30. 9. What will 36 bushels of corn cost, at 78. 6 d. per bushel › 33,10. 10. What cost 12 bbls. of ale, at 17 s. 6 d. per bbl.?-10,10. A. 66£. 108. 11. What will 5 cwt. 3 qrs. 21 lbs. of sugar cost, at $9,60 per 12. At $2,50 per yard, what will 5 yds. 2 qrs. of broadcloth cost?-1375. What will 4 yds. 1 qr. cost?-10625. Will 6 yda 9 qrs.?-16875. Ans. $41,25. 13. 5 cwt. 3 qrs. 16 lbs., at $4,20 per cwt. ?-2475. 14. 3 cwt. 1 qr. 7 lbs., at $3,60 per cwt.?-11925. 15. 4 yds. 2 qrs., at $2,10 per yd. ?-945. 36. 4 gals. 2 qts., at $3,40 per gal. ?–1530, A. $61,425. LXXVII. FELLOWSHIP. 1. Two boys, William and Thomas, trading with marbles, in company, gained 80 cents; William owned of the marbles, and Thomas; what was each one's part of the gain? 2. James and Rufus, owning a sled, in company, sold it for $3 more than it cost, that is, $3 gain; Rufus owned of it, and James; what was each one's share of the gain? Q. What is the RULE of FELLOWSHIP? A. When men are trading in company, it ascertains the gain or loss to be shared by each. Q. What is called STOCK, or CAPITAL? A. The money advanced or put in trade Q. What is called DIVIDEND? A. The gain or loss to be shared by cach. 1. Three men, A, B, and C, traded in company; A put in $200, B $400, and C $600; they gained $300: what was each man's share of the gain? In this example, it is evident, that B ought to have twice as much of the gain as A, for his stock is twice as much, and C 3 times as much as A; that is, each man's gain or loss ought to have the same relation to the whole gain of loss, as the money he put in has to the money they all put in. The same prin ciple will apply in all cases in which a number is to be divided into parts, which shall have a given relation, or ratio, to each other, as the dividing a bankrupt's estate among his creditors, apportioning taxes, &c. Hence, from the foregoing example, we derive the following proportions: A's stock, B's stock, $200 $400 1200 : 200 : 300 50, A's gain. $600 1200 400 300: 100, B's gain. Whole stock, $1200) 1200 600 :: 300 150, C's gain. 400 600 By ratios. These are 20%, 120%, 12%,,,; then, 300 x, that is, & of $300,$50, A's; of $300-$100, B'■, and of $300-$150, C's gain. Or, by analysis. If $1200 stock gain $300, then $1 stock will gain Tabo of $300,=120% = $1. Now, if $1 gain then of $200, A's stock, $50, A's gain; of $400, stock,=$100, B's rain; and † of $600, C's stock,= $150, C' gain. = This last method will generally be found the shortest, and best adapted to business; especially when there are several statements, in which all the first terms are alike, and all the third terms are alike. PROOF. It is plain, that, if the work be right, the amount of the shares of the gain or loss must be equal to the whole gain or loss; thus, in the last example, A's is $50+ B's $100 + Cs $150= $300, the whole gain." Q. What, then, is the ROLE? A. As the whole stock to each man's stock :: the whole gain: to each man's gain. 2. Three merchants, A, B, and C, gained, by trading in com pany, $200; A's stock was $150, B's $250, and C's $400; what was the gain on $1, and what was each man's share of the gain? A. The gain on $1 is $1; then, of $150= $37,50 A's; † of $250 = $62,50, B's; and of $400 = $100, C's. 3. A, B, and C, freight a ship with 270 tons; A shipped on board 96 tons, B 72, and C 102; in a storm, the seamen were obliged to throw 90 tons overboard; what was the loss on 1 ton? and how many tons did each lose? A. The loss on 1 ton is of a ton; A's, 32; B's, 24; C's, 34. 4. A and B trade in company, with a joint capital of $600; A put in $350,50, and B $249,50, and, by trading, they gained $120: what is the gain on $1, and what is each person's share of the gain? Ans. $t; A's, $70,10; B's, $49,90. 5. A ship, valued at $25200, was lost at sea, of which be longed to A, to B, and the remainder to C: what is the loss on $1? and how much will each man sustain, supposing $18000 of her to be ensured? Ans. ; A's, $2400; B's, $3600, and C's, $1200. Perform the following examples, in the same manner, by finding how much it is for $1, or unity. 6. A detachment, consisting of 5 companies, was sent into a garrison, in which the duty required 226 men a day the first company consisted of 162 men; the second, 153; the third, 144? the fourth, 117; and the fifth, 108; how many men must each company furnish, in proportion to the whole number of men? A. The proportion for 1 man is ; then, of 16254, first company; the second, 51: the third, 48; the fourth, 39; and the fifth, 36 men. 7. Two men, A and B, traded in company, with joint capi tal of $1000: they gained 400, of which A took $300, and B the remainder: what was each person's stock? Ans $1 guin zoquires 24 stock : A's, $750;. B's, $250. |