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.

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