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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.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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