2011 AMC 8 第 14 题

先试着解答 2011 AMC 8 第 14 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2011 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

14.

Colfax Middle School 有 270270 名学生,男生与女生的比为 5:45 : 4。Winthrop Middle School 有 180180 名学生,男生与女生的比为 4:54 : 5。两所学校举办舞会,所有学生都参加。舞会上女生占学生总数的几分之几?
There are 270270 students at Colfax Middle School, where the ratio of boys to girls is 5:4.5 : 4. There are 180180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5.4 : 5. The two schools hold a dance and all students from both schools attend. What fraction of the students at the dance are girls?
718\dfrac{7}{18}
715\dfrac{7}{15}
2245\dfrac{22}{45}
12\dfrac{1}{2}
2345\dfrac{23}{45}
答案:C
知识点:比与比例分数
小提示:
然后用女生总数除以 270+180270+180
Then divide the total number of girls by 270+180270+180.
大提示:
根据每所学校的比例求女生人数
Find the number of girls at each school from its ratio.
解答:
女生总数为 49⋅270+59⋅180=\dfrac{4}{9} \cdot 270 + \dfrac{5}{9} \cdot 180 = 120+100=220。 120 + 100 = 220\text{。}
学生总数为 270+180=450270 + 180 = 450,所以女生所占比例为 220450=2245\dfrac{220}{450} = \dfrac{22}{45}。
所以正确答案是 C。
The total number of girls is 49⋅270+59⋅180=\dfrac{4}{9} \cdot 270 + \dfrac{5}{9} \cdot 180 = 120+100=220. 120 + 100 = 220.
There are 270+180=450270 + 180 = 450 students total, so the fraction of girls is 220450=2245.\dfrac{220}{450} = \dfrac{22}{45}.
Thus, C is the correct answer.
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