AMC8 2011

AMC8 2011 · Q14

AMC8 2011 · Q14. It mainly tests Ratios & proportions, Averages (mean).

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?

Colfax中学的学生有270人，男孩与女孩比例为5:4。Winthrop中学的学生有180人，男孩与女孩比例为4:5。两校举办舞会，所有学生都参加。舞会上女孩占学生总数的几分之几？

(A) $\frac{7}{18}$ $\frac{7}{18}$

(B) $\frac{7}{15}$ $\frac{7}{15}$

(D) $\frac{1}{2}$ $\frac{1}{2}$

(E) $\frac{23}{45}$ $\frac{23}{45}$

Answer

Correct choice: (C)

正确答案：（C）

Solution

At Colfax Middle School, there are $\frac49 \times 270 = 120$ girls. At Winthrop Middle School, there are $\frac59 \times 180 = 100$ girls. The ratio of girls to the total number of students is $\frac{120+100}{270+180} = \frac{220}{450} = \boxed{\textbf{(C)}\ \frac{22}{45}}$

Colfax中学女孩有$\frac49 \times 270 = 120$人。Winthrop中学女孩有$\frac59 \times 180 = 100$人。女孩与总学生数的比例为$\frac{120+100}{270+180} = \frac{220}{450} = \boxed{\textbf{(C)}\ \frac{22}{45}}$

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