2. The sum of the ages of Tom and John is 23 , the sum of the ages of John and Alex is 24 and the sum of the ages of Tom and Alex is 25 . What is the sum of the squares of their three ages?
SOLUTION
434

Let the ages of Tom, John and Alex be $T, J$ and $A$ respectively. We have $T+J=23$ and $T+A=25$. Subtracting these equations we have $A-J=2$. Solving this, and $J+A=24$ simultaneously, we have $J=11, A=13$ and hence $T=12$. Therefore, the sums of the squares of their ages is $11^{2}+12^{2}+13^{2}=434$.