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
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.
The following figure shows the graph of the Diophantine equation
Five lattice points of the graph satisfy the constraints and