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Weighing the Baby

Age 14 to 16 Short Challenge Level:

When a mother was weighed holding her baby, the scales read $78\;\mathrm{kg}$.

When the nurse was weighed holding the baby, the scales read $69\;\mathrm{kg}$.

When the nurse and the mother stood on the scales together, the scales read $137\;\mathrm{kg}$.

What was the weight of the baby?

If you liked this problem, here is an NRICH task that 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.