AMC12 2012 12B, Problem 7

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 3rd red light and the 21st red light? Note: $1$ foot is equal to $12$ inches.

Solution: We know the repeating section is made of $2$ red lights and $3$ green lights. The 3rd red light would appear in the 2nd section of this pattern, and the 21st red light would appear in the 11th section. There would then be a total of $44$ lights in between the 3rd and 21st red light, translating to $45$ $6$-inch gaps. Since the question asks for the answer in feet, the answer is $\frac{45*6}{12} \rightarrow \fbox{22.5}$.

Answer: 22.5