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Math · Problem-Solving and Data AnalysisHard

A shirt is discounted by 30%30\%, and then an 8%8\% sales tax is applied to the discounted price. The final cost of the shirt is $37.80\$37.80. What was the original price, in dollars, of the shirt before the discount and tax?

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Answer: 50

A 30%30\% discount multiplies the price by 0.700.70, and the tax multiplies the result by 1.081.08. So 0.70×1.08×p=37.800.70 \times 1.08 \times p = 37.80, or 0.756p=37.800.756p = 37.80. Dividing gives p=50p = 50 dollars.

Combining the percents into a single 22%22\% discount (0.78p=37.800.78p = 37.80) gives about $48.46\$48.46, which ignores that the tax applies to the already-discounted price.

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