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Zorluk: OrtaPercentage Calculations

A supply store reduces the price of a generator by 20%20\%. During a clearance sale, this discounted price is reduced by an additional 25%25\%. If the final clearance price is $360\$360, what was the original price of the generator?

  1. A
    $540\$540
  2. $600\$600Cevap
  3. C
    $800\$800
  4. D
    $900\$900

Cevap

The original price of the generator was $600\$600.
The problem involves successive percentages. The first discount leaves 80%80\% of the original price. The second discount removes 25%25\% of that 80%80\%, leaving 75%75\% of 80%80\%, which mathematically is 0.80×0.75=0.600.80 \times 0.75 = 0.60. This means the final price is exactly 60%60\% of the original price. Dividing the final price of $360\$360 by 0.600.60 yields the correct original price of $600\$600.

Adım Adım Çözüm

1
Represent the original price as a variable and apply the first discount.
If the original price is xx, the price after a 20%20\% discount is x−0.20x=0.80xx - 0.20x = 0.80x.
A 20%20\% reduction means the buyer pays 80%80\% of the original price.
2
Apply the second discount to the newly reduced price.
The clearance price is 0.80x−(0.25×0.80x)=0.80x×0.75=0.60x0.80x - (0.25 \times 0.80x) = 0.80x \times 0.75 = 0.60x.
Successive discounts are applied to the previously discounted price, not the original price. Taking 25%25\% off means keeping 75%75\% of the current value.
3
Set up the equation with the given final price and solve for xx.
0.60x=3600.60x = 360, so x=3600.60=600x = \frac{360}{0.60} = 600.
The final represented percentage (60%60\%) equals the final dollar amount ($360\$360), allowing us to isolate the original price.

Anahtar Kavram

Successive Percentage Decreases
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Konular

Percentage Calculations

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