A complete course of arithmetical examples and exercises - Softcover

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1882 edition. Excerpt: ...is TTjs of vTM of jTjQ of the original cost--the original cost? in other words, is it true that..,, 144. 85, 85,, thevalueo£iooof rooof ioo = 1! i.e., is 144 x 85 x 85 = 100 x 100 x 100 = 1000000? Answer, NO. But it is clear that when the answer has been subtracted from 100, a number (corresponding to the 85 above) will be found which when multiplied by itself and then by 144 will give 1000000; What Is That Number? To find it we must evidently (1) divide 1000000 by 144;. 1000000 we thus get--... (2) find the square root of this quotient; the number is thus found to be equal to Combining (i.) and (ii.) we thus get 100 100-A. 100-A. _ C x 144 = TOO of 100 ofC Dividing each side of the equation by C, we now get 100 _ 100-A 100-A 144-100 x 100.. 100 x 100 x 100 = 144 x (100-A) x (100-A). See Ex. XIII. i.e. 1000000 = 144 (10000-200 A + A') dividing each side of the equation by 4, we get 250000 = 36 (10000-200 A + AJ) i.e. 250000 = 360000-7200 A + 36 A'.-. 36 A'-7200 A = 250000-360000 =-110000 I10000 110000 hence A-200 A + 10000 = 10000---5.-.A-100= /2M0OO + 500--6.,TM + 500.-. A = 100 _-g = 100 + 831 = 183J or 16J Answer--16J per cent. N.B.--The other quantity, viz. 183£, is mathematically correct also, but if, by the terms of the question, a man should lose 183J per cent., it is clear that he must not only sell it for nothing, but also give the purchaser a bonus to take it for nothing. Example LXXXVII. A crew rowing with the stream gets from A to B in 50 minutes; coming against the stream they row from B to A in 65 minutes; compare the rates of the stream and the boat. The difference in the time = 65 mins.-50 mins. = 15 mins. In one case the stream helps the boat; in the other case it retards it by an equal amount; the speed...

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