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
Dec 15, 2016

Ratio of girls to the total number of chorus members is 3:5

Explanation:

The ratio of boy to girls is color(blue)2:color(red)3

You can find the number of boys and girls by dividing the total number color(brown)50 by the sum of color(blue)2 and color(red)3, and then multiply the quotient by color(blue)2 to find the numbers of boys, and color(red)3 to find the number of girls.

We need to find the number of girls to find the ratio of girls to the total number of chorus members ->color(brown)50

color(brown)50/(color(blue)2+color(red)3)=50/5=10

Number of girls = 10(color(red)3)=30

The ratio of girls to the total number of chorus members is 30:color (brown)50 which can be simplified to 3:5

Dec 15, 2016

The answer is 3:5.

Explanation:

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

The long way:

Scale the ratio 2:3 so that the numbers on either side sum to 50.

2+3=5, and 50-:5=10, so we scale our ratio by a factor of 10.

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

So there are a total of color(blue)"20 boys" and color(purple)"30 girls" in the choir of color(green)"50 students".

This means the ratio of girls-to-"all members" is color(purple)30:color(green)50. We then scale this ratio down so it's in smallest terms. The greatest common factor of 30 and 50 is 10:

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

Thus, the ratio of girls-to-everyone is 3:5.

The short way:

The ratio color(blue)"2 boys" : color(purple)"3 girls" means we can divide the chorus into groups of 2+3=color(green)"5 students" where each group has color(blue)"2 boys" and color(purple)"3 girls" (with no students left over).

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 color(blue)"2 boys" : color(purple)"3 girls", each group also has a ratio of color(purple)"3 girls" : color(green)"5 students", and so does the whole chorus.

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.