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Difficulty: MediumDiscounts and Sale Prices

A cafe owner is purchasing a commercial espresso machine. Supplier A lists the machine for $2,000\$2,000 with a single 30%30\% discount. Supplier B lists the identical machine for $2,400\$2,400 with successive discounts of 25%25\% and 20%20\%. How much money will the owner save by purchasing the machine from the less expensive supplier?

  1. A
    $385\$385
  2. $40\$40Answer
  3. C
    $80\$80
  4. D
    $360\$360

Answer

The owner will save $40 by choosing Supplier A.
Supplier A's final price is 1,400(whichis1,400 (which is 2,000 minus a 600discount).SupplierB′sfinalpriceis600 discount). Supplier B's final price is 1,440 (calculated by first reducing 2,400by252,400 by 25% to get 1,800, and then reducing 1,800by201,800 by 20% to get 1,440). The difference between the two prices is $40, making Supplier A the less expensive option by that amount.

Step-by-Step Solution

1
Calculate the final price for Supplier A.
$2,000×0.30=$600\$2,000 \times 0.30 = \$600 discount. $2,000−$600=$1,400\$2,000 - \$600 = \$1,400.
A single discount is taken directly from the initial price.
2
Calculate the price after the first discount for Supplier B.
$2,400×0.25=$600\$2,400 \times 0.25 = \$600 discount. $2,400−$600=$1,800\$2,400 - \$600 = \$1,800.
The first of the successive discounts is applied to the original listing price.
3
Calculate the price after the second discount for Supplier B.
$1,800×0.20=$360\$1,800 \times 0.20 = \$360 discount. $1,800−$360=$1,440\$1,800 - \$360 = \$1,440.
The second discount must be applied to the new subtotal, not the original price.
4
Find the difference between the two final prices.
$1,440−$1,400=$40\$1,440 - \$1,400 = \$40.
Subtracting the lower price from the higher price gives the total savings.

Key Concept

Calculating successive discounts and comparing final sale prices.
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Topics

Discounts and Sale Prices

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