Baby's weight
Weekly Problem 36 - 2008
Weighing the baby at the clinic was a problem. The baby would not keep still so we had to hold her while on the scales. Can you work out our combined weight?
Weighing the baby at the clinic was a problem. The baby would not keep still so we had to hold her while on the scales. Can you work out our combined weight?
Age
11 to 14
Challenge level
Problem
Weighing the baby at the clinic was a problem. The baby would not keep still and caused the scales the wobble.
So I held the baby and stood on the scales while the nurse read off $78 \; \text{kg}$.
Then the nurse held the baby while I read off $69 \; \text{kg}$.
Finally I held the nurse while the baby read off $137 \; \text{kg}$.
What is the combined weight of all three (in $\text{kg}$)?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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?