AMC 8 2008 Problem 20

AMC8 2008 年第 20 题

比与比例★★★☆☆

The students in Mr. Neatkin's class took a penmanship test. Two-thirds of the boys and

\displaystyle \frac{3}{4}

of the girls passed the test, and an equal number of boys and girls passed the test. What is the minimum possible number of students in the class?

Neatkin 先生班上的学生参加了某个笔试。三分之二的男孩和

\displaystyle \frac{3}{4}

的女孩通过了这个笔试，且通过这个笔试的男孩和女孩个数是一样的。则这个班最少可能是多少个学生？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Let

b

be the number of boys and

g

be the number of girls.

\frac23 b = \frac34 g \Rightarrow b = \frac98 g

For

g

and

b

to be integers,

g

must cancel out with the denominator, and the smallest possible value is 8. This yields 9 boys. The minimum number of students is 8+9=17.

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