Tom was asked to guess a fraction. The sum of 1/2 of the number and

Question

1/3 of its denominator is 30. If Tom subtracts 36 from its denominator, the
fraction becomes 1/3. What is the fraction that Tom was asked to guess?
(Leave your answer in the simplest form)

Answer 1

N= Numerator
D=Denominator

n/2 + d/2 = 30
d-36=d/3

d=3d-108
(use bring over method)
-2d=-108
-d=-54
d=54

n/2+d/3=30
n/2+54/3=30
n=24

Hence, N/D = 24/54 ~ 4/9.