Bank teller swaps dollars and cents on a cheque

A cashier paying out a cheque mixes up the units, handing over the dollar amount as cents and the cent amount as dollars. The customer, who started with no money, walks off without checking, buys a sweet for $5$ cents, and then finds he holds exactly double the cheque's value. What was the cheque worth?

$31.63. If the cheque is $D$ dollars and $C$ cents, he received $100C+D$ cents, so $100C+D-5=2(100D+C)$, i.e. $98C=199D+5$. The only solution with $0\le C,D\le 99$ is $D=31$, $C=63$; check: $63.31-0.05=63.26=2\times31.63$.