Word problem

Question

The denominator of a fraction is two more than the numerator.  If both numerator and denominator are increased by three, the simplified result is 19/20.  Find the original fraction.  (Do not simplify)

Answer 1

n represents the numerator

n + 2 represents the denominator

 

(n + 3) / (n + 2 + 3) = 19/20

(n + 3) / (n + 5) = 19/20           combine like terms

20(n + 3) / (n + 5) = 19            multiply both sides by 20

20(n + 3) = 19(n + 5)               multiply both sides by (n + 5)

20n + 60 = 19n + 95                distribute

n + 60 = 95                              subtract 19n from both sides

n = 35                                      subtract 60 form both sides