2009 AMC 10B Problem 8

Question

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?

12

17

20

25

35

After March the price is

(1.2)(0.8)(1.25)

times the starting price

April must divide out a factor of

1.2

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.

Problem 8 in other years