Fraction problem

Question

In a certain fraction, the numerator is 3 less than the denominator. If 5 is added to both the numerator and the denominator, the resulting fraction is 4/5. Find the original fraction. 

Answer 1

Let d = denominator. So we set up the fraction as [(d-3) +5]/(d+5) is equal to 4/5.

Simplify the numerator of the left side of the fraction. (d+2)/(d+5) = 4/5

Cross multiply. 4(d+5) = 5(d+2)

Distribute. 4d+20 = 5d +10

Combine like terms and solve for d. d = 10

 

Denominator of the original fraction was 10 and the numerator is d-3 = 7. So the original fraction was 7/10.