mathschallenge.net

Problem

Three different positive integers add to make sixteen. The two smallest numbers add to make the biggest number. How many different solutions can you find?

Solution

Let the integers be a, b and c such that a b c.

Therefore a + b + c = 16.

But a + b = c, so c + c = 2c = 16, hence c = 8.

So solutions are: (1,7,8), (2,6,8) and (3,5,8)