Question

The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

Answer 1

Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is

The sum of the numerator and denominator of the fraction is 3 less than twice the denominator. Thus, we have

If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Thus, we have

So, we have two equations

Here x and y are unknowns. We have to solve the above equations for x and y.

By using cross-multiplication, we have

Hence, the fraction is.