18. Put in store at one time 500 pounds of hemp; at another time 3800 pounds; and at another 2005 pounds. Having withdrawn 3473 pounds, what quantity remains in store? Ans. 2832 pounds 19. Three persons propose to purchase a manufactory, valued at 25850 dollars; A agrees to pay 5000 dollars, B twice as much as A. and C the remainder. What sum will C have to pay? Ans. 10850 dollars. 20. A planter sold cotton amounting to 3460 dollars, and out of these proceeds purchased groceries for 150 dollars, and other provisions for 375 dollars; how much of the first sum had he remaining? Ans. 2935 dollars. 21. A cabinet-maker sold furniture to the amount of 4000 dollars, and received in payment, at different times, 200 dollars, 475 dollars, and 904 dollars. How much of the debt remains to be paid? Ans. 2421 dollars. 22. A bought of B 875 acres of land for 23400 dollars. For 500 acres of the tract he paid 11379 dollars; how many acres were in the remainder of the tract? and for what sum was it purchased? Ans. 375 acres; and 12021 dollars. 23. A merchant exchanges a stock of goods worth 6725 dollars, and a house worth 3120 dollars, for a tract of land valued at 5900 dollars,-the farmer paying the balance in money. What sum must the merchant receive? Ans. 3945 dollars. 24. A gentleman purchased at one time 7 acres, and at another time 12 acres of land, at 234 dollars an acre; what did the whole amount to? The whole amounted to 234 dollars multiplied by the sum of 7 and 12; that is, 234 dollars X 19. 234 Ans. 4446 dollars. When the Multiplier is 13, 14, or 15, &c., the operation may be abbreviated thus :-multiply by the units figure, 9 in this example, and set the first product figure, 6, one place to the right of the units in the multiplicand; and, in this order, add the product to the multiplicand. In like manner we may multiply by 1 with O's and a significant figure annexed, as 103, 1004, &c.; observing to set the first product figure one more place to the right of the multiplicand than there are intervening O's in the multiplier. 25. A merchant sold a piece of cloth containing 45 yards, another piece containing 57 yards, and another containing 63 yards, at 14 dollars a yard. What did the whole amount to? Ans. 2310 dollars. 26. Farmer A had in wheat 205 acres, which produced 27 bushels per acre; and farmer B had 320 acres, which produced 19 bushels per acre. What quantity of wheat was raised by them both? Ans. 11615 bushels. 27. A speculator bought 150 head of cattle, and 47 mules. He made a profit of 13 dollars a head on the former, and 17 on the latter; what was gained by the speculation? Ans. 2749 dollars. 28. A has 340 acres of land worth 18 dollars an acre, and B has 239 acres worth 22 dollars an acre. How many acres have the two together? and what is the value of the whole? Ans. 579 acres; and 11378 dollars. 29. One manufacturer exported 234 bales of cloth, each containing 103 yards; another exported 209 bales, each containing 107 yards. Which of the two exported the greater quantity? and by how many yards? Ans. The first, by 1739 yards. 30. Two persons start from the same place, at the same time, and travel in contrary directions. One proceeds at the rate of 39 miles per day, and the other at the rate of 44 miles per day; how many miles will they be apart at the end of 21 days? The number of miles they will be apart, is the sum of 39 miles and 44 miles multiplied by 21; that is, 83 miles × 21. 83 166 Ans. 1743 miles. When the Multiplier is 21, 31, or 41, &c., the operation may be abbreviated thus :-multiply by the tens figure, 2 in this example, and set the first product figure, 6, under the tens figure of the multiplicand, and thus add the product to the multiplicand. In like manner we may multiply by any significant figure with O's and a unit annexed, as 201, 3001, &c.; observing to set the first product figure one more place to the left of the units in the multiplicand than there are intervening O's in the multiplier. 31. A bought of B, 475 acres of land at 31 dollars per acre, 236 acres of which he sold to C at 18 dollars, and the remainder to D at 41 dollars per acre. What did A gain or lose by these transactions? Ans. Lost 678 dollars. bales of linen; each bale What was 32. An importer bought 124 contained 24 pieces, and each piece 21 yards. the whole number of pieces? and the whole number of yards? Ans. 2976 pieces; 62496 yards. 33. A farmer has three tracts of land. The first and second contain 280 acres each, and the third contains twice as much as both the other two; how many acres does the farmer own? and what would the whole amount to at 201 dollars per acre? Ans. 1680 acres; 337680 dollars. 34. A gave B 3 horses, and 31 head of cattle, for 51 bar rels of flour, and 301 barrels of corn. A sold the flour at 6 dollars, and the corn at 3 dollars, a barrel; while B sold his horses at 120 dollars, and his cattle at 17 dollars, each. Which of the two gained by the trade? and how much? Ans. A gained 322 dollars. 35. A has 339 acres of land, and B has 240 acres. Allowing each tract to be worth 54 dollars per acre, how much does the whole value of A's land exceed that of B's? The value of A's land exceeds the value of B's by the product of 54 dollars multiplied by the excess of 339 above 240 ; that is, by 54 dollars × 99. 5400 Ans. 5346 dollars. When the Multiplier is any number of 9's, the operation may be abbreviated thus :-annex as many O's to the multiplicand as there 9's in the multiplier, and from the result subtract the multiplicand. In this example, the annexing of 00 to the 54 produces 100 times 54 (29); then 54 subtracted leaves 99 times 54. 36. What would be the sum of the products obtained by multiplying 375 dollars by 9, five hundred and thirty seven dollars by 99, and six hundred and forty one dollars by 999? Ans. 696897 dollars 37. An ironmonger bought 99 tons of iron at 39 dollars per ton, 19 tons at 43 dollars per ton, and 20 tons at 40 dollars per ton. What would he gain or lose by selling the whole at 41 dollars per ton? Ans. He would gain 180 dollars. 38. A merchant bought 290 yards of cloth at 9 dollars per yard. Having sold 137 yards of it, at 14 dollars per yard, and 81 yards, at 15 dollars per yard; what would he make on the whole by selling the remainder at 16 dollars per yard? Ans. 1675 dollars. 1 39. A planter sold 139 bales of cotton, at an average of 41 dollars per bale. Out of the proceeds he bought 29 mules, at 100 dollars each, and 4 pair of oxen, at 81 dollars a pair; what sum had he left from the sale of his cotton? Ans. 2475 dollars. 40. A sends to market 209 tons of coal; B sends as much as A, wanting 10 tons; and C sends as much as A and B together. What is each man's proceeds of sale, at 13 dollars per ton? Ans. A's 2717 dollars; B's 2587; C's 5304. 41. A farmer bought land from A at 60 dollars an acre, and the same quantity from B at 85 dollars an acre. The whole amounted to 53215 dollars; how many acres did he buy from each? To buy one acre from each, required 60 dollars + 85 dollars, that is, 145 dollars; then the number of acres bought from each, is the number of times that 145 is contained in 53215. 145) 53215 (367 acres. 971 1015 0000 The operation of dividing, by several figures, may be abbreviated, by subtracting the products of the divisor and quotient figures mentally. In thus subtracting, we add as many tens as may be necessary to the upper figure, and then add as many units to the next product. Thus, We say 145 in 532, 3 times; 3 times 5 is 15; 15 from 22 leaves 7, which we set down; 3 times 4 is 12, and 2 make 14; 14 from 23 leaves 9; 3 times 1 is 3, and 2 make 5; 5 from 5 leaves nothing. Bringing down the 1 from the dividend, we say 145 in 971, 6 times; 6 times 5 is 30; 30 from 31 leaves 1; 6 times |