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Without knowing which is older, you cannot assign their ages. But one is 10 and the other is 5.

The idea here is to write two equations, one for the sum of the ages (B + E = 15), one for the difference. Then, solve both equations simultaneously. There are several ways to do this; for example, you can solve one of the equations for "B", and replace that variable in the other equation.

x + y = 15

x = y +5

(y+5) + y = 15

2y + 5 = 15

2y = 10

y = 5 (the younger child), x = y+5 = 10 (the older child).

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Q: The sum of Barbara's and Ed's ages is 15 years. The difference is 5 years. How old are Barbara and Ed?
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