A school fund-raiser has students selling candy bars in two sizes: and . Anthony collected but forgot what he sold. If remembers selling at least candy bars and at least of the jumbo size, how many possible combinations could he have sold?

Source: NCTM Math Teacher 2008

**SOLUTION**

Let be the number of smaller size candy bars and the number of jumbo size.

must be even in order to make a whole dollar amount and not a fractional amount.

We stop here because of the constraint

Anthony could have sold possible combinations.

*Alternative solution*

The following figure shows the graph of the Diophantine equation

Five lattice points of the graph satisfy the constraints and

.

**Answer**: 5

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