Sue Pinion, Lisa Stueve, Sandy McAdams

Check Problem

A man writes a check for d dollars and c cents. The clerk cashed the check and gave him c dollars and d cents. After spending 5 cents, he has twice the amount of the original check. What was the original check?

Let the original check be 100 d + c.
Therefore the equation representing the situation would be 2 (100 d +c) = 100 c + d -5 which reduces to the equation 199 d + 5 = 98 c.
This poses a problem for the solutions under the constraints that we use in the high school classroom. We usually require two equations to solve for two unknowns.

A spreadsheet was created to check values of d and c for which the equation would be true.
The first column contains a fixed value of d. The second column calculates the value of 199 d + 5. The third column represents a variable value of c filled in consecutive order. The fourth column calculates the value of 98 c. The fifth column calculates the difference in the two calculated values in columns two and four. When this difference is zero, then the solution is achieved.

Values were entered into column one for d starting with 1. It was quickly ovious that a much larger odd value should be used. After several tries with larger numbers, it was discovered that d= 31 and c = 63 were the solutions. Therefore the check was written for $31.63.

To open a spreadsheet for the check problem, click here.

To open a demonstration of the Euclidean Algorithm to locate a solution, click here.

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