Question

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?

Answer 1

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)`.