The denominator of a fraction is greater than its numerator by 12.if the numerator is decreased by 2 and the denominator is increased by 7 the new fraction is equivalent with 1/2 find the fraction

Answer 1

Let x = the numerator of the fraction. Since the denominator is 12 bigger, it is x+12 and the fraction is

x/(x+12)

Add 2 to the numerator: x+2. Add 7 to the denominator: x+12+7 = x + 19, and it equals 1/2:

(x+2)/(x+19) = 1/2

Cross multiply: 2(x+2) = x + 19

Solve for x. Once you've found x, the fraction is x/(x+12)