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There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4. There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5. The two schools hold a dance and all students from both schools attend. What fraction of the students at the dance are girls?

User Wasd
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1 Answer

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Given:

Total number of students at Colfax Middle School = 270

Ratio of boys to girls is 5:4.

Total number of students at Winthrop Middle School = 180

Ratio of boys to girls is 4:5.

The two schools hold a dance and all students from both schools attend.

To find:

The fraction of the students at the dance are girls

Solution:

There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4.


5+4=9

Number of boys
=270* (5)/(9)=150

Number of girls
=270* (4)/(9)=120

There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5.


4+5=9

Number of boys
=180* (4)/(9)=80

Number of girls
=180* (5)/(9)=100

Now,

Total number of students in both schools
= 270+180


= 450

Total number of girls in both schools
= 120+100


= 220

The fraction of the students at the dance are girls is


\text{Required fraction}=\frac{\text{Total number of girls in both schools}}{\text{Total number of students in both schools}}


\text{Required fraction}=(220)/(450)


\text{Required fraction}=(22)/(45)

Therefore, the required fraction is
(22)/(45).

User Linyun Liu
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