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 $=270\times \dfrac{5}{9}=150$

Number of girls $=270\times \dfrac{4}{9}=120$

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

$4+5=9$

Number of boys $=180\times \dfrac{4}{9}=80$

Number of girls $=180\times \dfrac{5}{9}=100$

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

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

$\text{Required fraction}=\dfrac{220}{450}$

$\text{Required fraction}=\dfrac{22}{45}$

Therefore, the required fraction is $\dfrac{22}{45}$.