36. (x-5) (x − 2) — (x − 5) (2x − 5) + (x + 7) (x − 2) = 0. 37. 3-x-2(x-1) (x + 2) = (x − 3) (5 — 2x). EXA 38. 39. 40. AMPLES OF EQUATIONS OF THE FIRST DEGREE. CH. IX. 79 x − 3 − (3 −x) (x + 1) = (x − 3) (1 + x) + 3 − x. (3x-2) (2x-3) = + 2 = 0. 3) + 3). 14 6x + 2 56 14 X. PROBLEMS WHICH LEAD TO SIMPLE EQUATIONS WITH ONE UNKNOWN QUANTITY. 167. We shall now apply the methods already given to the solution of some problems, and thus exhibit to the student specimens of the use of Algebra. In a problem certain quantities are given, and certain others, which have some assigned relations to them, are to be found. The relations are usually expressed in ordinary language in the enunciation of the problem, and the method of solving the problem may be thus described in general terms:-denote the unknown quantities by letters, and express in Algebraical language the relations which hold between the unknown quantities and the given quantities; we shall thus obtain equations from which the values of the unknown quantities may be derived. We shall now give some examples. 168. The sum of two numbers is 89 and their difference is 31; find the numbers. Let x denote the less number, then the greater number is 31+x; thus since their sum is 89, we have Thus the less number is 29, and the greater is 29 +31, that is, 60. 169. A bankrupt owes B twice as much as he owes A, and C' as much as he owes A and B together; out of £300 which is to be divided among them, what should each receive? Let x denote the number of pounds which A should receive; then 2x is what B should receive; and x + 2x, that is 3x, is what C should receive. The whole sum they receive is £300; thus, therefore A should receive £50, B £100, and C £150. 170. Divide a line 21 inches long into two parts, such that one may be three-fourths of the other. 3.x х Let x denote the number of inches in one part, then denotes 4 the number of inches in the other part; thus, Thus one part is 12 inches long and the other 9 inches. 171. If A can perform a piece of work in 8 days, and B in 10 days, in what time will they perform it together? T. A. 6 |