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?

$\dfrac{7}{18}$

$\dfrac{7}{15}$

$\dfrac{22}{45}$

$\dfrac{1}{2}$

$\dfrac{23}{45}$

Solution:

The total number of girls is $\dfrac{4}{9} \cdot 270 + \dfrac{5}{9} \cdot 180 =$ $120 + 100 = 220.$

There are $270 + 180 = 450$ students total, so the fraction of girls is $\dfrac{220}{450} = \dfrac{22}{45}.$

Thus, C is the correct answer.

2011 AMC 8 Problem 14

Solution:

Problem 14 in Other Years