2009 AMC 12B Problem 7

Problem 7 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?

Show solution

Solution

After January through March the price is

1.2 \cdot 0.8 \cdot 1.25 = 1.2

times the original. To return to the original, April must multiply by

\dfrac{1}{1.2},

a decrease of

1 - \dfrac{1}{1.2} = \dfrac{1}{6} \approx 16.7\%.

To the nearest integer,

x = 17.

Thus, the correct answer is B.