CHAPTER XVI.
Problems leading to Fractional and Literal Equations.
166. We here give some problems which lead to equations with fractional and literal coefficients.
Ex. 1. Find two numbers which differ by 4, and such that one-half of the greater exceeds one-sixth of the less by 8.
Let x represent the smaller number, then x + 4 represents the greater. One-half of the greater is represented by {1}{2}(x + 4), and one-sixth of the less by {1}{6}x.
Hence {1}{2}(x + 4) - {1}{6}x = 8; multiplying by 6, 3x + 12 — x = 48; 2x = 36 ; x = 18, the less number, and x + 4 = 22, the greater.
Ex. 2. A has $180, and B has $84; after B has won from A a certain sum, A has then five-sixths of what B has ; how much did B win ?
Suppose that B wins x dollars, A has then 180 — x dollars, and B has 84 + x dollars.
Hence 180 - x = {5}{6}(84 + x) ; 1080 -6x = 420 + 5x, 11x = 660 ; x = 60. Therefore B wins $60.
EXAMPLES XVI.
1. Find a number such that the sum of its sixth and ninth parts may be equal to 15.
2. What is the number whose eighth, sixth, and fourth parts together make up 13?
3. There is a number whose fifth part is less than its fourth part by 3: find it.
