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AMC 12 Mock Exam 2 Problem 3

Problem 3 of 25

A store raises the price of a jacket by 25%25\%. Later, during a sale, it lowers the new price by x%x\%, and the sale price turns out to be 10%10\% below the original price. What is xx?

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Solution

If the original price is PP, the sale price is 1.25P(1−x100)=0.9P1.25P\left(1-\frac{x}{100}\right)=0.9P. So 1−x100=0.91.25=0.721-\frac{x}{100}=\frac{0.9}{1.25}=0.72 and x=28x=\boxed{28}.

Tagged: successive percent changes