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Zorluk: OrtaDiscounts and Sale Prices

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

Cevap: 500 $

Cevap

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×0.80×0.90=360x \times 0.80 \times 0.90 = 360. Simplifying the left side yields 0.72x=3600.72x = 360, and dividing by 0.720.72 correctly identifies the original price as $500.

Adım Adım Çözüm

1
Set up an expression for the price after the first discount.
0.80x0.80x
A 20%20\% discount means the buyer pays 100%−20%=80%100\% - 20\% = 80\% of the original price xx.
2
Set up an expression for the price after the second discount.
0.72x0.72x
An additional 10%10\% discount means the buyer pays 90%90\% of the already discounted price. Multiplying 0.90×0.80x0.90 \times 0.80x gives 0.72x0.72x.
3
Set the final expression equal to the sale price and solve for the original price.
0.72x=360⇒x=5000.72x = 360 \Rightarrow x = 500
This isolates the original price, xx, finding the initial value before any markdowns.

Anahtar Kavram

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

Discounts and Sale Prices

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