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

AI Thread Summary
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 There is a recurring overpayment amount of \$85.00 so \$85.00 was to be withdrawn from the 25% of \$400.00 for a total of \$15.00.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 There is a recurring overpayment amount of $85.00 so $85.00 was to be withdrawn from the 25% of $400.00 for a total of $15.00.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?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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