Algebraical Problems, Producing Simple and Quadratic Equations, with Their Solutions; Designed As an Introduction to the Higher Branches of Analytics

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. 1824 edition. Excerpt: ...Now A sold for a crown one-third of an ell more than B did. 'How many ells did each sell for a crown? 16. Three Merchants, A, B, and C, made a joint stock, by which they gained a sum less than that stock by .80. A's share of the gain was .60; and his contribution to the stock was of.17 more than Jb's. Also B and C together contributed .325. How much did each contribute? Let x = the number of pounds that A contributed;.-. x--17= the number that B contributed, and 325--(x--17) = 342-x = the number that C contributed; S25-Hx = the whole stock, and 325 + x--80 = 245 + x = the whole gain;.-. 325+x: x:: 245+x: 60, and x5 + 245x = 60x+19500;. by transposition, x2 + 185x= 19500; completing the square, x + 185x +--H = 19500 34225 112225 +--=----; 4 4 185 335 extracting the root, x H = +, and i = 75, or--260; the stocks of A, B and C were 75, 58, and 267 pounds, respectively. 18. A body of men were formed into a hollow square, three deep, when it was observed that with the addition of 25 to their number, a solid square might be formed, of which the number of men in each side would be greater by 22 than the square root of the number of men in each side of the hollow square. Required the number of men in the hollow square. Let = the number of men in a side of the hollow squares 19. A Mercer bought a number of pieces of two different kinds of silk for .9%. 3s. There were as many pieces bought of each kind, and as many shillings paid per yard for them as a piece of that kind contained yards. Now 2 pieces, one of each kind, together measured 19 yards. How many yards were there in each? Let x = the number of yards in one piece; and.-. =the number of pieces, and also the number of shillings per yard; 19--x = the number in the...