March 21, 2005
Problem of the Month

The Confused Bank Teller

A confused bank teller transposed the dollars and cents when he cashed a check for Mrs. P, giving her dollars instead of cents and cents instead of dollars.

After buying a newspaper for 50 cents, Mrs. P noticed that she had left exactly three times as much as the original check.

What was the amount of the check? (Note: 1 dollar = 100 cents.)

Solution to the Problem:

The check was for $18.56.

Let x be the number of dollars in the check, and y be the number of cents.
Then 100y + x - 50 = 3(100x + y).
Therefore 97y - 299x = 50.

This is called a Diophantine equation.
There are many integer solutions, but we need one where 0 <= x <= 99 and 0 <= y <= 99.
One such pair of numbers is y = 56, x = 18.
I used the table feature of a graphing calculator to make certain that x = 18 was the only integral solution between x = 0 and x = 99.

So the check was for $18.56.

Correctly solved by:

1. Jeffrey Gaither	Winchester, Virginia
2. Jim Arrison	Norristown, Pennsylvania
3. David & Judy Dixon	Bennettsville, South Carolina
4. James Alarie	University of Michigan -- Flint, Flint, Michigan
5. António Baptista	Lisboa, Portugal
6. Joshbeen Grewal	Washington, DC
7. Carrie Wilson	Ticonderoga, New York
8. Mike Singer	Winchester, Virginia
9. Huseyin Pehlivan	Karadeniz Teknik üniversitesi Trabzon, Turkey
10. Trey Mason	Winchester, Virginia
11. Daniel Gardiner	Winchester, Virginia
12. Ben Swartz	Winchester, Virginia
13. Charles Washington	Winchester, Virginia
14. Emily Auerbach	Columbus, Georgia
15. Mandy Auerbach	Columbus, Georgia
16. Sharina Broughton	Old Dominion University, Norfolk, Virginia
17. Larry Schwartz	Trumbull, Connecticut

Send any comments or questions to: David Pleacher