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2019 AMC 8 Question 22

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Re: 2019 AMC 8 Question 22
by John Lensmire - Thursday, April 9, 2020, 5:00 PM

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.