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?

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.

Hnmmmn not sure