Challenge Level

You could try 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?