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2019 AMC 8 Question 22

2019 AMC 8 Question 22
ZongEllen - 2020年04月9日 Thursday 01:17

A store increased the original price of a shirt by a certain percent and then decreased the new price by the same amount. Given that the resulting price was 84% of the original price, by what percent was the price increased and decreased?

Re: 2019 AMC 8 Question 22
LensmireJohn - 2020年04月9日 Thursday 17:00

Since the problem is about percentages, it is safe to assume a price for the shift, say it costs $100$ (this will be easier to calculate with). Then after the price change it costs $84$.

One way to solve the problem is to use algebra. Let $x$ be the percent it is raised and then decreased and write an equation to solve for $x$.

It is also possible to use the answer choices and see which one works. For example, answer choice B is $20\%$. This doesn't work because$$100\times 120\% \times 80\% = 96,$$which is not 84.