2014 AMC 8 Problems/Problem 7

Problem

There are four more girls than boys in Ms. Raub's class of $28$ students. What is the ratio of number of girls to the number of boys in her class?

$\textbf{(A) }3 : 4\qquad\textbf{(B) }4 : 3\qquad\textbf{(C) }3 : 2\qquad\textbf{(D) }7 : 4\qquad \textbf{(E) }2 : 1$

Solution 1

We can set up an equation with $x$ being the number of girls in the class. The number of boys in the class is equal to $x-4$ . Since the total number of students is equal to $28$ , we get $x+x-4=28$ . Solving this equation, we get $x=16$ . There are $16-4=12$ boys in our class, and our answer is $16:12=\boxed{\textbf{(B)}~4:3}$ .

Solution 2

To make the amount of boys and girls equal, 28 - 4 = 24. 24/2 = 12. The girls would need to be 12 + the 4 that we subtracted = 16. The boys would be 12. The ratio of girls to boys would be 16 : 12, but simplified would be 4 : 3. Thus, the answer is 4 : 3.

~MiracleMaths

2014 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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2014 AMC 8 Problems/Problem 7

Contents

Problem

Solution 1

Solution 2

See Also