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Two Number Lines

Stage: 2 Challenge Level: Challenge Level:1

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:

0-10 horizontal number line


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

0-10 vertical number line

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:

graph with axes 0-10


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

graph with point (4, 6) marked


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

graph with point (9, 3) marked


If Max and Mandy both moved the same distance along and up, where could the counter be?