The numerator of a fraction exceeds the denominator by 5...

Question

The numerator of a fraction exceeds the denominator by 5. If the numerator is decreased by 4 and the denominator is increased by 3, the resulting fraction is equal to 4/5. Find the original fraction.

(sorry, I wrote the wrong fraction the first time posting this question)

Answer 1

The numerator of a fraction exceeds the denominator by 5 means (x+5) / x.

Decreasing the numerator by 4 means x + 5 - 4 = x+1. Increasing the denominator by 3 means x + 3. So the resulting fraction is:

(x+1) / (x+3) = 4/5

Cross multiply and solve for x, then plug the value of x into (x+5) / x to get the original fraction.