The sum of the present ages of Nick and Stephen is 56 years. Four years ago, Stephen's age was half of Nick's age at that time. What is Nick's present age (in years)?
36
Let the present ages of Nick and Stephen be N and S years. The first condition gives N + S = 56.
Four years ago their ages were N – 4 and S – 4, and Stephen's age was half of Nick's, so \(S - 4 = \frac{N - 4}{2}\), i.e. N – 4 = 2S – 8, so N = 2S – 4.
Substituting in N + S = 56: (2S – 4) + S = 56, so 3S = 60, S = 20 and N = 56 – 20 = 36.
Check: 36 + 20 = 56 years; four years ago the ages were 32 and 16, and 16 is exactly half of 32.
Hence, 36.
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