Guess a fraction

Tom was asked to guess a fraction. The sum of 1/2 the numerator and 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 simplest form)

Result

d =  72
n =  12
f =  0.167

Solution:

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

2d+3n = 180
d-3n = 36

d = 72
n = 12

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