2012 AMC 12B Problem 7

Problem 7 of 25EasierAlgebra

Small lights are hung on a string

6

inches apart in the order red, red, green, green, green, red, red, green, green, green, and so on continuing this pattern of

2

red lights followed by

3

green lights. How many feet separate the

3

rd red light and the

21

st red light? Note:

1

foot is equal to

12

inches.

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Solution

The lights repeat in blocks of

5,

so consecutive blocks start

5\cdot6=30

inches, or

2.5

feet, apart. Each block has one odd-numbered red light beginning it. The

3

rd red light begins the

2

nd block and the

21

st red light begins the

11

th block. The distance between them is

(11-2)\cdot2.5=22.5

feet. Thus, the correct answer is E.