Math Corner: Wardrobe Overcharge

By Jason Gershman •

Question: Student Razor Q. Shark wants a new wardrobe for the fall semester. He makes 11 separate shopping trips during the semester to his favorite clothing store buying only shirts and/or shorts and nothing else on each shopping trip. Razor pays with his credit card on each shopping trip. At this store, each shirt costs $13 and each pair of shorts costs $5 (all prices include tax).

At the end of the semester, Razor reviews his credit card bills and discovers 12 charges from this store instead of 11 so Razor knows that one of them was charged to him in error. The amounts of each charge are:

$43, $102, $62, $57, $133, $97, $92, $47, $52, $123, $77, $36

Based on the value of the charges, which dollar amount charged was the amount charged in error?

Show Answer ▼

$47 is not possible (There are no whole numbered ordered pairs where 13x + 5y = 47….the other 11 values are possible.)

“Math Corner” is a contest that appears in each issue of The Current and is a collaboration between NSU’s Department of Mathematics | NSU Halmos College of Arts and Sciences | NSU and NSU’s Department of Communication, Media, and the Arts | Halmos College of Arts and Sciences | NSU. Contest submissions to the Math Corner question in the Current’s latest issue can be sent to jgershma@nova.edu up until the date the next issue is published. Prizes are awarded at the end of the academic year.