Fraction Word problem

Question

the numerator of a fraction is 4 less than its denominator. If 1 is added to the numerator and denominator, the resulting fraction equals 1/3.  What was the original fraction?

Answer 1

Let numerator = x - 4

Let denominator = x

 

Adding 1 to both the numerator and denominator gives

 

numerator = (x - 4) + 1 = x - 3

denominator = x + 1

 

This makes the new fraction equal to 1/3.

 

(x - 3) / (x + 1) = 1 / 3

 

 

Solve for x.  Cross-multiply.

 

x + 1 = 3(x - 3)

 

x + 1 = 3x - 9

 

2x = 10

 

  x = 5

 

 

The original fraction is then    1/5.