2009 AMC 10B Problem 8

Problem 8 of 25EasierAlgebra

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?

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Solution

Let

p

be the starting price. After March the price is

(1.2)(0.8)(1.25)p=1.2p.

The April drop must return it to

p,

so it removes

0.2p,

a fraction

x=100\cdot\dfrac{0.2p}{1.2p}=\dfrac{100}{6}\approx16.7.

To the nearest integer,

x=17.

Thus, the correct answer is B.