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A fraction becomes 1/2 when 1 is subtracted from its numerator, and becomes 1/3 when 8 is added to its denominator. Find the fraction.

Competition practiceAlgebra

A3/5
B2/5
C4/7
D5/9

Step-by-Step Solution

Let

n / d . (n - 1) / d = 1/2

→

d = 2 n - 2. n / (d + 8) = 1/3

→

3 n = d + 8

. Substituting:

3 n = 2 n + 6

→

n = 6, d = 10

. Fraction = 6/10 = 3/5.

Answer: A) 3/5

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