Question

In a certain fraction, the denominator is 4 less than the numerator. if 3 is added to both the numerator and the denominator, the resulting fraction is equivalent to 2. what was the original fraction (not written in lowest terms?

Answer 1

Make a system of equation before finding the numbers. d stands for denominator and n stands for the numerator.
⇒ d = n - 4 (first equation)
⇒ (n + 3)/(d + 3) = 2 (second equation)

Simplify the second equation
(n + 3) / (d + 3) = 2
(n + 3) = 2(d + 3)
n + 3 = 2d + 6

Solve the equation system by subtituting d with n-4 from the first equation into the second equation
n + 3 = 2d + 6
n + 3 = 2(n - 4) + 6
n + 3 = 2n - 8 + 6
n + 3 = 2n - 2
n - 2n = -2 - 3
-n = -5
n = 5
The original numerator is 5

Find the original denominator by inputing 5 as numerator to one of the equation
d = n - 4
d = 5 - 4
d = 1
The original denominator is 1

So the original fraction is 5/1