What is the answer to this equation?

Question

Anupa's favorite fraction is equal to . The sum of the numerator and denominator of Anupa's favorite fraction is . What is the difference between the numerator and denominator of Anupa's favorite fraction?

Answer 1

If an improper fraction is equal to 5/3 , then it must have a common factor in the numerator and denominator. Call that common factor k. So the fraction could be 5k/3k (for example 10/6 or 15/9). We are told that the numerator and denominator sum to 160:

5k + 3k = 160

8k = 160

k = 20

Than means her favorite fraction is 100 / 60. The difference between numerator and denominator is:

100 - 60 = 40.