Question

The denominator of a fraction is four more than three times the numerator. If both numerator and denominator are increased by four, the simplified result is 9/25. Find the original fraction. (Do NOT simplify.)

Answer 1

Let the numerator = x. Then,

The fraction is x/(3x+4).

If both the numerator and denominator are increased by 4, the fraction will be (x+4)/(3x+8), which, according to the question is equal to 9/25. So,

(x+4)/(3x+8) = 9/25

25(x+4) = 9(3x+8)

25x + 100 = 27x + 72

2x = 28

x = 14

Thus, the numerator is 14 and the denominator is (3*14 + 4), which is equal to 46. So the fraction is 14/46.