NRICH: Lattice Points on a Line

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

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.

Age 11 to 14

Algebra & Pre-Algebra, Functions & Graphs, Linear Equations
Middle School, High School, Educator

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