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Weighing the Baby

Stage: 4 Short Challenge Level: Challenge Level:1

Let $m$ be my weight, $b$ be the baby's weight and $n$ be the nurse's weight.

We have
$$
\begin{align}
m+b&=78\\
b+n&=69\\
m+n&=137\;.
\end{align}
$$
We can add all three equations together like this:
$$(m+b)+(b+n)+(m+n)=78+69+137\;.$$
It follows that $2(m+b+n)=284$ and hence $m+b+n=142$. So the combined weight is $142\;\mathrm{kg}$.

For an extra challenge can you find the weights of each person?

This problem is taken from the UKMT Mathematical Challenges.