An electronics store is liquidating its marine equipment inventory. A high-frequency boat … — Armed Services Vocational Aptitude Battery (ASVAB)

An electronics store is liquidating its marine equipment inventory. A high-frequency boat radar system is marked down by $20\%$ from its original price. During a special weekend clearance event, an additional $10\%$ is taken off the already discounted price. If the final sale price of the radar system is $\$360$ , what was the original price of the system in dollars?

Answer: 500 $

Answer

The original price of the radar system was $500.

The correct answer is found by setting up an equation with successive multipliers for each discount phase:

x \times 0.80 \times 0.90 = 360

. Simplifying the left side yields

0.72x = 360

, and dividing by

0.72

correctly identifies the original price as $500.

Step-by-Step Solution

Set up an expression for the price after the first discount.

0.80x

20\%

discount means the buyer pays

100\% - 20\% = 80\%

of the original price

x

Set up an expression for the price after the second discount.

0.72x

An additional

10\%

discount means the buyer pays

90\%

of the already discounted price. Multiplying

0.90 \times 0.80x

gives

0.72x

Set the final expression equal to the sale price and solve for the original price.

0.72x = 360 \Rightarrow x = 500

This isolates the original price,

x

, finding the initial value before any markdowns.

Key Concept

Calculating successive discounts and setting up an equation to find the original pre-sale price.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic