# 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

Let $g$ being the number of girls in the class. The number of boys in the class is equal to $g-4$. Since the total number of students is equal to $28$, we get $g+g-4=28$. Solving this equation, we get $g=16$. 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

## Video Solution (CREATIVE THINKING)

~Education, the Study of Everything

## Video Solution

https://youtu.be/fjbcgj5W30E ~savannahsolver

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 