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Difficulty: HardDiscounts and Sale Prices

A restaurant manager wants to purchase a commercial refrigerator with a list price of $3,200\$3,200. Supplier A offers a single discount of 38%38\% off the list price. Supplier B offers a 25%25\% discount off the list price, followed by an additional 15%15\% discount applied to the newly reduced price.

How many dollars does the manager save by choosing the supplier with the lower final price instead of the other supplier?

Answer: 56 $

Answer

56
Supplier A's final price is $1,984\$1,984 (after a 38%38\% reduction from $3,200\$3,200). Supplier B's final price is $2,040\$2,040 (after a 25%25\% reduction to $2,400\$2,400, followed by a 15%15\% reduction). Choosing Supplier A over Supplier B saves the manager $2,040−$1,984=$56\$2,040 - \$1,984 = \$56.

Step-by-Step Solution

1
Calculate Supplier A's final sale price.
$1,984\$1,984
Supplier A offers a single 38%38\% discount. 100%−38%=62%100\% - 38\% = 62\%. 0.62×$3,200=$1,9840.62 \times \$3,200 = \$1,984.
2
Calculate Supplier B's price after the initial discount.
$2,400\$2,400
Supplier B offers an initial 25%25\% discount. 100%−25%=75%100\% - 25\% = 75\%. 0.75×$3,200=$2,4000.75 \times \$3,200 = \$2,400.
3
Calculate Supplier B's final sale price.
$2,040\$2,040
Supplier B offers an additional 15%15\% off the reduced price. 100%−15%=85%100\% - 15\% = 85\%. 0.85×$2,400=$2,0400.85 \times \$2,400 = \$2,040.
4
Find the difference between the two final prices.
$56\$56
Subtracting Supplier A's price from Supplier B's price gives the total savings: $2,040−$1,984=$56\$2,040 - \$1,984 = \$56.

Key Concept

Calculating successive discounts and comparing final sale prices.
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Topics

Discounts and Sale Prices

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