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.

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