MHB Solve Algebra Word Problem: Overpayment Amount of \$85.00

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The March bill was $400.00, with 25% due, equating to $100.00. A recurring overpayment of $85.00 should have resulted in a payment of $15.00. Instead, an incorrect calculation led to a payment of $78.75 after subtracting the overpayment from the total bill. This results in an overpayment of $63.75 compared to the correct amount owed. The discussion highlights confusion regarding the total overpayment based on differing calculations.
moore
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March bill was \$400.00 for 25% to be paid of that. There is a recurring overpayment amount of \$85.00 so \$85.00 was to be withdrawn from the 25% of \$400.00 for a total of \$15.00.

\$400.00 x .25 = \$100.00

\$100.00 - \$85.00 = \$15.00

However, rather than doing that; the following was done:

\$400.00 - \$85.00 = \$315.00
\$315.00 x .25 = \$78.75

How much has been overpaid now?
 
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moore said:
March bill was $400.00 for 25% to be paid of that. There is a recurring overpayment amount of $85.00 so $85.00 was to be withdrawn from the 25% of $400.00 for a total of $15.00.

$400.00 x .25 = $100.00

$100.00 - $85.00 = $15.00

However, rather than doing that; the following was done:

$400.00 - $85.00 = $315.00
$315.00 x .25 = $78.75

How much has been overpaid now?
Pretty straight forward, isn't it? According to your original computation, you should have paid 15.00. But if you paid according to the second (incorrect) calculation you would pay 78.75. You would have overpaid by 78.75- 15.00= 63.75.
 
HallsofIvy said:
Pretty straight forward, isn't it? According to your original computation, you should have paid 15.00. But if you paid according to the second (incorrect) calculation you would pay 78.75. You would have overpaid by 78.75- 15.00= 63.75.

\$63.75?; but \$85.00 were overpaid and now $78.75 were overpaid.

Wouldn't it be more?
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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