2009 AMC 10B Problems/Problem 8

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(Redirected from 2009 AMC 12B Problems/Problem 7)

The following problem is from both the 2009 AMC 10B #8 and 2009 AMC 12B #7, so both problems redirect to this page.

Problem

In a certain year the price of gasoline rose by $20\%$ during January, fell by $20\%$ during February, rose by $25\%$ during March, and fell by $x\%$ during April. The price of gasoline at the end of April was the same as it had been at the beginning of January. To the nearest integer, what is $x$

$\mathrm{(A)}\ 12\qquad\mathrm{(B)}\ 17\qquad\mathrm{(C)}\ 20\qquad\mathrm{(D)}\ 25\qquad\mathrm{(E)}\ 35$

Solution

Let $p$ be the price at the beginning of January. The price at the end of March was $(1.2)(0.8)(1.25)p = 1.2p.$ Because the price at the of April was $p$ , the price decreased by $0.2p$ during April, and the percent decrease was $x = 100 \cdot \frac{0.2p}{1.2p} = \frac {100}{6} \approx 16.7.$ So to the nearest integer $x$ is $\boxed{17}$ . The answer is $\mathrm{(B)}$ .

2009 AMC 10B (Problems • Resources)
Preceded by Problem 7	Followed by Problem 9
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2009 AMC 12B (Problems • Resources)
Preceded by Problem 6	Followed by Problem 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

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2009 AMC 10B Problems/Problem 8

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