CH. 6 review #2

Question

If a certain number is added to the numerator and denominator of 7/5, the result is 5/4. Find the number?

Answer 1

We start with the fraction 7/5

 

we add the same number to the numerator and denominator

 

7 + x / 5 + x, and we set this expression equal to 5/4

 

so, we have (7 + x) / (5 + x) = 5/4

 

we cross multiply to get 4(7 + x) = 5(5 + x)

 

expanding, we get 28 + 7x = 25 + 5x

 

combining, we get 28 - 25 = 5x - 4x

 

solving, 3 = x

 

Proof: 7 + 3 / 5 + 3 = 10/8 = 5/4