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Difficulty: EasyFractions, Decimals, and Percents Arithmetic

A clothing store reduced the original price of a jacket by 20%20\%. During a promotional event, the store offered an additional 15%15\% discount off the reduced price. If the final price of the jacket was $102\$102, what was the original price of the jacket, in dollars?

Answer: 150 dollars

Answer

The original price of the jacket was $150.
To find the original price, express the final price as a decimal multiplier of the original price. A 20%20\% discount leaves 80%80\% of the original price (0.800.80). An additional 15%15\% discount off the reduced price leaves 85%85\% of that amount (0.850.85). The overall price multiplier is 0.80×0.85=0.680.80 \times 0.85 = 0.68. Setting 0.68×Original Price=1020.68 \times \text{Original Price} = 102 gives an original price of 1020.68=150\frac{102}{0.68} = 150 dollars.

Step-by-Step Solution

1
Determine the combined price multiplier after both successive discounts.
The first discount leaves 80%80\% (0.800.80) of the original price, and the second discount leaves 85%85\% (0.850.85) of that reduced price. The combined multiplier is 0.80×0.85=0.680.80 \times 0.85 = 0.68.
Successive percentage discounts are multiplicative rather than additive.
2
Set up an equation equating the final discounted price to 102102.
0.68×P=1020.68 \times P = 102, where PP represents the original price.
The final price is 68%68\% of the original base price.
3
Solve for the original price PP.
P=1020.68=1020068=150P = \frac{102}{0.68} = \frac{10200}{68} = 150.
Dividing the final amount by the net decimal multiplier yields the original value.

Key Concept

Successive percentage change calculation
Estimated Time:1m 0s
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Topics

Fractions, Decimals, and Percents Arithmetic

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