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Difficulty: EasyPercent Change and Interest

The price of a jacket was increased by 20%20\%. During a clearance sale, the new price was reduced by 10%10\%. What was the net percentage increase in the price of the jacket from its original value?

  1. A
    18%18\%
  2. B
    10%10\%
  3. 8%8\%Answer
  4. D
    12%12\%
  5. E
    30%30\%

Answer

An 8%8\% net increase
Applying successive percentage changes requires multiplying the growth/decay factors. A 20%20\% increase corresponds to a multiplier of 1.201.20, and a 10%10\% decrease corresponds to a multiplier of 0.900.90. The net multiplier is 1.20×0.90=1.081.20 \times 0.90 = 1.08, which represents a net increase of 8%8\% over the original price.

Step-by-Step Solution

1
Assume a convenient original price to track percentage changes easily.
Let the original price of the jacket be $100\$100.
Choosing $100\$100 as a base makes calculating percentages straightforward.
2
Calculate the price after the 20%20\% increase.
$$100+0.20×$100=$120\$\$100 + 0.20 \times \$100 = \$120.
The price increases by 20%20\% of the original price.
3
Calculate the price after the 10%10\% clearance discount.
$$120−0.10×$120=$108\$\$120 - 0.10 \times \$120 = \$108.
The discount of 10%10\% applies to the intermediate price of $120\$120, not the original $100\$100.
4
Determine the net percentage change from the original price.
$108−$100$100×100%=8%\frac{\$108 - \$100}{\$100} \times 100\% = 8\%.
Comparing the final price of $108\$108 to the initial price of $100\$100 gives a net increase of 8%8\%.

Key Concept

Successive Percent Change
Estimated Time:45s
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Topics

Percent Change and Interest

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