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

Answer:

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

Answer:

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#.