Respuesta :
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.
[tex]5+4=9[/tex]
Number of boys [tex]=270\times \dfrac{5}{9}=150[/tex]
Number of girls [tex]=270\times \dfrac{4}{9}=120[/tex]
There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5.
[tex]4+5=9[/tex]
Number of boys [tex]=180\times \dfrac{4}{9}=80[/tex]
Number of girls [tex]=180\times \dfrac{5}{9}=100[/tex]
Now,
Total number of students in both schools [tex]= 270+180[/tex]
[tex]= 450[/tex]
Total number of girls in both schools [tex]= 120+100[/tex]
[tex]= 220[/tex]
The fraction of the students at the dance are girls is
[tex]\text{Required fraction}=\dfrac{\text{Total number of girls in both schools}}{\text{Total number of students in both schools}}[/tex]
[tex]\text{Required fraction}=\dfrac{220}{450}[/tex]
[tex]\text{Required fraction}=\dfrac{22}{45}[/tex]
Therefore, the required fraction is [tex]\dfrac{22}{45}[/tex].
