Weighing the baby

Weighing the baby at the clinic was a problem. Can you work out the total weight of the baby, the nurse and me from the information given?
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Problem



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.