The ratio of the number of girls to the number of boys in a class of 24 students is $3: 5$. How many fewer girls than boys are in the class?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8

Part B: Each correct answer is worth 6.
Solution 1

The ratio of the number of girls to the number of boys is $3: 5$, so for every 3 girls there are 5 boys and $3+5=8$ students.

That is, the number of girls in the class is $\frac{3}{8}$ of the number of students in the class.

Since the number of students in the class is 24 , the number of girls is $\frac{3}{8} \times 24=\frac{72}{8}=9$.

The remaining $24-9=15$ students in the class must be boys.

Therefore, there are $15-9=6$ fewer girls than boys in the class.

## Solution 2

The ratio of the number of girls to the number of boys is $3: 5$, so if there are $3 x$ girls in the class then there are $5 x$ boys.

In total, there are 24 students in the class, so $3 x+5 x=24$ or $8 x=24$ and so $x=3$.

The number of girls in the class is $3 x=3(3)=9$ and the number of boys in the class is $5 x=5(3)=15$.

Therefore, there are $15-9=6$ fewer girls than boys in the class.

## Solution 3

The ratio of the number of girls to the number of boys is $3: 5$, so for every 3 girls there are 5 boys and $3+5=8$ students.

That is, $\frac{3}{8}$ of the number of students in the class are girls and $\frac{5}{8}$ of the number of students are boys.

Thus, the difference between the number of boys in the class and the number of girls in the class is $\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}$ of the number of students in the class.

Therefore, there are $\frac{1}{4} \times 24=6$ fewer girls than boys in the class.

ANSWER: (D)