2014 CEMC Gauss (Grade 8) Problems/Problem 10

Problem

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?

$\textbf{(A)}\ 2 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 5 \qquad\textbf{(D)}\ 6 \qquad\textbf{(E)}\ 8$

Let there be $3x$ girls and $5x$ boys in the class, as the ratio of girls to boys is $3:5$ . The total is then $3x + 5x = 8x$ .

We know that the class has $24$ students in total. Thus, we have:

$8x = 24$

$x = 3$

There is then $5x - 3x = 2x$ fewer girls than boys, or $2 \times 3 = \boxed {\textbf {(D) } 6}$ fewer girls.

~anabel.disher