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Difficulty: EasyPercents and Percent Change

During a weekend sale, a store reduced the price of a bicycle by 20%20\%. If the sale price of the bicycle is $160\$160, what was the original price, in dollars, of the bicycle?

  1. A
    $128\$128
  2. B
    $180\$180
  3. C
    $192\$192
  4. $200\$200Answer

Answer

The original price of the bicycle was $200\$200.
The correct answer is $200\$200. A discount of 20%20\% means that the sale price of $160\$160 is 80%80\% of the original price (100%−20%=80%100\% - 20\% = 80\%). Setting up the equation 0.80×P=1600.80 \times P = 160, where PP is the original price, and solving for PP gives P=1600.80=200P = \frac{160}{0.80} = 200.

Step-by-Step Solution

1
Express the relationship between the original price and the sale price using the discount percentage.
The sale price represents 80%80\% of the original price because a 20%20\% discount was applied (100%−20%=80%100\% - 20\% = 80\%).
Establishing the percentage value of the sale price relative to the original price is necessary to set up the equation.
2
Set up an equation with the original price, represented by PP.
0.80×P=1600.80 \times P = 160
Since the sale price is 80%80\% of the original price, multiplying the original price by 0.800.80 must equal the sale price of $160\$160.
3
Solve for the original price, PP, by dividing both sides of the equation by 0.800.80.
P=1600.80=200P = \frac{160}{0.80} = 200
Dividing the sale price by the decimal representation of its percentage of the original price isolates the variable and calculates the original price.

Key Concept

Percents and Percent Change
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Topics

Percents and Percent Change

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