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Difficulty: HardDiscounts and Sale Prices

A woodworker is purchasing a bulk supply of lumber with a regular total price of $800\$800. The supplier offers two different discount options for the purchase:

Option 1: A $150\$150 instant rebate on the regular price, followed by a 15%15\% discount on the remaining balance.
Option 2: A 25%25\% discount on the regular price, followed by an additional 5%5\% discount on the reduced price.

What is the positive difference in the final sale price between the two options?

  1. $17.50\$17.50Answer
  2. B
    $7.50\$7.50
  3. C
    $135.00\$135.00
  4. D
    $44.50\$44.50

Answer

The correct difference between the two options is $17.50\$17.50.
Option 1 evaluates to $552.50\$552.50 by first subtracting the $150\$150 rebate and then taking 15%15\% off the remaining $650\$650. Option 2 evaluates to $570.00\$570.00 by first taking 25%25\% off the original $800\$800, yielding $600\$600, and then taking an additional 5%5\% off the $600\$600, which is $30\$30. The difference between $570.00\$570.00 and $552.50\$552.50 is $17.50\$17.50.

Step-by-Step Solution

1
Calculate the price for Option 1 after the instant rebate.
$800−$150=$650\$800 - \$150 = \$650
The rebate is a flat amount subtracted from the initial regular price before any percentage discounts are applied.
2
Calculate the final price for Option 1 after the 15% discount.
$650−($650×0.15)=$650−$97.50=$552.50\$650 - (\$650 \times 0.15) = \$650 - \$97.50 = \$552.50
The 15%15\% discount applies to the remaining balance of $650\$650.
3
Calculate the price for Option 2 after the initial 25% discount.
$800−($800×0.25)=$800−$200=$600\$800 - (\$800 \times 0.25) = \$800 - \$200 = \$600
The first discount is applied directly to the regular price.
4
Calculate the final price for Option 2 after the additional 5% discount.
$600−($600×0.05)=$600−$30=$570.00\$600 - (\$600 \times 0.05) = \$600 - \$30 = \$570.00
Successive discounts are applied to the newly reduced price, not the original price.
5
Calculate the positive difference between the two final prices.
$570.00−$552.50=$17.50\$570.00 - \$552.50 = \$17.50
Subtracting the smaller final price from the larger final price provides the difference.

Key Concept

Calculating successive discounts, rebates, and comparing multiple-step financial scenarios.
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Topics

Discounts and Sale Prices

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