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?
Age
14 to 16
Challenge level
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.
Student Solutions
Answer: 5 kg
Let $m$ be the mother's weight, $b$ be the baby's weight and $n$ be the nurse's weight.
We have
$$
\begin{align}
m+b&=78\\
b+n&=69\\
m+n&=137.
\end{align}
$$
Adding all three equations together
$$(m+b)+(b+n)+(m+n)=78+69+137.$$ It follows that $2(m+b+n)=284$ and hence $m+b+n=142$
Since mother and nurse together weigh $137\;\mathrm{kg}$ the baby must weigh $5\;\mathrm{kg}$
Removing the nurse and mother
$n+m=137$, and$\ n+b+m+b = 78+69\\
\Rightarrow n+m+2b=147$
$\therefore 2b=10\Rightarrow b=5$