Question

If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. What is the numerator of the fraction?

Answer 1

If when the numerator of a fraction is increased by 3, the fraction becomes 3/4 and when the denominator is decreased by 7, the fraction becomes 1, then the numerator of the fraction would be 9.

Answer 2

let the numerator be x and denominator be y :-

then (x + 3) / y = 3/4.....(1)
also
x / (y - 7) = 1........(2)

From (2) x = y - 7

Substitute for x in equation (1):-

(y - 7 + 3) / y = 3/4

(y - 4) / y = 3/4
3y = 4(y-4)
3y = 4y - 16
y = 16

x = 16-7 = 9

Check to see if this fits equation (1)
(9+3) / 16 = 12/16 = 3/4

So the numerator x is 9.