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Difficulty: MediumDiscounts and Sale Prices

A commercial photographer is purchasing a new studio lighting kit. The original retail price of the kit is $1,200\$1,200. The camera supply store is currently offering a 25%25\% seasonal discount on all studio equipment. In addition, the photographer receives a 10%10\% professional discount, which is applied to the already reduced price. What is the final price of the lighting kit before sales tax?

Answer: 810 $

Answer

The final price of the lighting kit is $810\$810.
The correct calculation requires applying the first discount to find a new subtotal, and then applying the second discount to that new subtotal. Applying 25%25\% off $1,200\$1,200 yields $900\$900. Applying the 10%10\% professional discount to the new base of $900\$900 reduces the price by another $90\$90, resulting in a final price of $810\$810.

Step-by-Step Solution

1
Calculate the first discount amount.
25%25\% of $1,200\$1,200 is $300\$300.
The seasonal discount applies to the original retail price.
2
Find the intermediate reduced price.
$1,200−$300=$900\$1,200 - \$300 = \$900.
Subtracting the first discount gives the new base price before the second discount.
3
Calculate the second discount amount.
10%10\% of $900\$900 is $90\$90.
The professional discount applies to the already reduced price, not the original price.
4
Determine the final price.
$900−$90=$810\$900 - \$90 = \$810.
Subtracting the second discount from the intermediate price gives the final amount paid.

Key Concept

Calculating successive discounts requires applying the second percentage to the new, already discounted price, rather than the original amount.
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Topics

Discounts and Sale Prices

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