Question

If a certain fraction, the denominator is 4 less than the numerator. If 3 is added to both the numerator and denominator, the resulting fraction is equal to 9/7.Find the original fraction ​

Answer 1

Step-by-step explanation:

Let numerator of the fraction be x and denominator be y.

According to the first condition:

y = x - 4..... (1)

According to the second condition:

$\frac{x + 3}{y + 3} = \frac{9}{7} \\ 7(x + 3) = 9(y + 3) \\ 7x + 21 = 9y + 27 \\ 7x + 21 - 27 = 9y \\ 7x - 6 = 9y......(2) \\ from \: equations \: (1) \: and \: (2) \\ 7x - 6 = 9(x - 4) \\ 7x - 6 = 9x - 36 \\ 36 - 6 = 9x - 7x \\ 30 = 2x \\ x = \frac{30}{2} \\ x = 15 \: \implies \: y = 15 - 4 = 11 \\ hence \: x = 15 \: and \: y = 11 \\ thus \: the \: required \: fraction \: is \: \frac{15}{11}$