Weighing Scales
Age
14 to 16
Challenge level
Can you work out how many spheres will balance a single pyramid?
Problem
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Two pyramids and a sphere on one side of a pair of scales will just balance a cube on the other side.
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A sphere and a cube together will just balance three pyramids.
How many spheres will just balance a single pyramid?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 2
A pyramid weighs $p$, a sphere weighs $s$ and a cube weighs $c$.
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$2p + s = c$
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$s + c = 3p$, but $c=2p+s$ so: $$\begin{align}s+(2p+s)&=3p\\
\Rightarrow\ 2s+2p&=3p\\
\Rightarrow\ 2s&=p\end{align}$$