Problem-Solving and Data AnalysisVery hardOriginal price from a discount then tax
Problem-Solving and Data Analysis practice question
A jacket is sold at a 15% discount, and then 8% sales tax is added to the discounted price. The customer pays $91.80. What was the original price of the jacket, in dollars?
Answer: 100
Let P be the original price. After the discount it costs 0.85P; after tax, 1.08 × 0.85P = 0.918P. So 0.918P = 91.80 and P = 100.
Common wrong answers
- If you answered 85
- 85 is the DISCOUNTED price (before tax) of a $100 jacket. The question asks for the original price.
- If you answered 108
- 108 applies only the tax to 100, or treats 91.80 as the pre-discount amount. Undo both steps: divide 91.80 by 0.918.
- If you answered 98.71
- 98.71 treats the two changes as a single −7% (−15% + 8%). Percent changes multiply: 0.85 × 1.08 = 0.918, not 0.93.
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