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?
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
