Word problem

Question

^{The denominator of a fraction is 2 more than the denominator. If the numerator is decreased by 3 and the denominator is increased by 5, the resulting fraction is equal to 2/3. Find the original fraction.}

Answer 1

x

-----

x+2

x+3 2

------ = ----

x+7 3

3(x+3) = 2(x+7)

3x + 9 = 2x + 14

x + 9 = 14

x = 5

5/7 becomes 8/12 = 2/3

so the original fraction is 5/7;

adding 3 and 5 to the numerator and denominator respectively produces 8/12 = 2/3