# There are 50 students in a middle school chorus. The ratio of boys to girls in the chorus is 2:3. What is the ratio of girls to the total number of chorus members?

##### 2 Answers

Ratio of girls to the total number of chorus members is

#### Explanation:

The ratio of boy to girls is

You can find the number of boys and girls by dividing the total number

We need to find the number of girls to find the ratio of girls to the total number of chorus members

Number of girls

The ratio of girls to the total number of chorus members is

The answer is

#### Explanation:

We assume the chorus is made up of only boys and girls.

## The long way:

Scale the ratio

#(2 times 10) : (3 times 10)=20:30#

So there are a total of

This means the ratio of girls-to-"all members" is

#(30-:10):(50-:10)=3:5#

Thus, the ratio of girls-to-everyone is

## The short way:

The ratio

That means the ratio of boys-to-girls in each group will match the ratio of boys-to-girls in the whole chorus. Same goes for *any ratio* we may seek, including the ratio of girls-to-everyone.

Since each group has a ratio of

And that's it. All we had to do was go from

#color(blue)2:color(purple)3#

to

#color(purple)3:(color(blue)2+color(purple)3)=color(purple)3:color(green)5# .