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Lattice Points on a Line

Age 11 to 14 Short Challenge Level:

A point whose x and y coordinates are both whole numbers is called a lattice point.

How many lattice points that lie on the line $3x+4y=59$ are there in the first quadrant (where both x and y coordinates are positive)?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.