Question

the denominator of a fraction is 3 less than the numerator. If 5 is added to the numerator and denominator, the result is 5/6. Find the sum of the numerator and denominator of the original fraction.

Answer 1

X=numerator
y=denominator
the sum of numerator and denominator=x+y
we suggest this system of equations:

y=x-3
(x+5) / (y+5)=5/6

we solve this system of equation by substitution method.
(x+5) / (x-3+5)=5/6
(x+5) / (x+2)=5/6
6(x+5)=5(x+2)
6x+30=5x+10
6x-5x=10-30
x=-20

y=x-3=-20-3=-23

Teh sum of the numerator an denominator=-20+(-23)=-43

Answer:    -43