Question

The numerator and the denominator of a fraction are thirteen and fifty, respectively. When a certain number is added to this numerator and subtracted from this denominator, the resulting fraction has a numerator to denominator ratio of two to one. What is the number?

Answer 1

(13 + x)/(50 - x ) = (2/1)
Cross Multiply
2(50-x) = 1(13 + x)
100 - 2x = 13 + x
add 2x to both sides
100 -2x + 2x = 13 + x + 2x
100 = 13 + 3x
Subtract 13 from both sides
100 - 13 = 13 - 13 + 3x
87 = 3x
divide both sides by 3
29 = x

(13 + 29)/(50-29) = 42/21 = 2 to 1 ratio

Answer 2

The correct answer is 29.