# The Square of My Age

Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

If you add the square of Thom's age to Lauren's age the total is 62.

If you add the square of Lauren's age to Thom's age the total is 176.

How old are Thom and Lauren?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

**Answer**: Thom is $7$ and Lauren is $13$

The square of Thom's age is at most $62$, so Thom is at most $7$. The square of Thom's age is therefore at most $49$, so Lauren is at least $13$.

The square of Lauren's age is at most $176$, so Lauren is at most $13$. Therefore Lauren must be $13$, and Thom must be $7$.

And $114 = 2\times57 = 3\times38 = 6\times19