Katie's history class has 24 students. If the ratio of boys to girls is 3:1, how many more boys are there than girls in the class?

Question

mathstudent55 · Answer

A ratio of 3:4 can be expressed as a fraction, $\dfrac{3}{4} $

Let's look at some numbers that are in a ratio of 3:4

$\dfrac{30}{40} $, $\dfrac{6}{8} $, $\dfrac{9}{12} $

Ok so far?

anonymous · Answer

ok

anonymous · Answer

i got the answer but thnx

mathstudent55 · Answer

Each of those numbers is in a ratio of 3:4 because each one is written as a fraction that can be reduced to $\dfrac{3}{4} $.

For example, for $\dfrac{30}{40}$, this is how you'd reduce it.

$\dfrac{30}{40} = \dfrac{3}{4} \times \dfrac{10}{10} = \dfrac{3}{4} \times \dfrac{\cancel{10}}{\cancel{10}} = \dfrac{3}{4}$

mathstudent55 · Answer

You can express the ratio $\dfrac{3}{4}$ as $\dfrac{3x}{4x} $.

If numbers in a ratio add to a sum, you express it like this:

3x + 4x = sum

In your case the ratio is 3:1, so you'd do

3x + x = 24.

Solve for x.

Then 3x is the number of boys and x is the number of girls. Then subtract.

mathstudent55 · Answer

You're welcome.