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The Square of My Age

Age 11 to 14 Short Challenge Level:

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.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.