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?

Question

Mathematics

Jaiden Nash

28 November, 13:41

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?

+5

Answers (1)

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Justice Matthews · 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