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## 'Two Number Lines' printed from http://nrich.maths.org/

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Number Lines before this problem.

Max and Mandy both had number lines. Max's number line went along
from left to right like this:

Mandy's number line went up and down like this:

Max and Mandy both started at zero on their number lines. Max made
a secret jump along his number line and then moved on seven and
landed on $10$. How long was his secret jump?

Mandy made a jump of three and another secret jump. She landed on
$6$. How long was her secret jump?

Max and Mandy decided to put their number lines together. Their
teacher gave them some squared paper. They had made a graph. It
looked like a bit like this:

Max moved four along and Mandy moved six up. They put a counter on
the place they landed. Now their graph looked like this:

How far had each of them moved along and up from $0$ to get the
counter to the place marked on the grid below?

If Max and Mandy both moved the same distance along and up, where

could the counter
be?