2014 AMC 8 Problem 7

Attempt Problem 7 of the 2014 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

7.

There are four more girls than boys in Ms. Raub’s class of 2828 students. What is the ratio of the number of girls to the number of boys in her class?
3:4 3 : 4
4:3 4 : 3
3:2 3 : 2
7:4 7 : 4
2:1 2 : 1
Answer: B
Concepts:ratio and proportionlinear equation
Small hint:
Let the number of boys be bb.
Big hint:
Then the number of girls is b+4b+4, and the total is 2828.
Solution:
Let xx be the number of boys in the class. This means that there are x+4x + 4 girls. As there are 2828 students, we know that: x+x+4=282x=24x=12.\begin{align*} x + x + 4 &= 28\\ 2x&=24 \\ x&=12. \end{align*} Therefore, the ratio of girls to boys is 16:12=4:3.16 : 12 = 4 : 3.
Thus, B is the correct answer.
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