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