2007 AMC 10B 第 16 题

Question

一位老师给一个班考试，其中

10\%

的学生是低年级生，

90\%

是高年级生。考试平均分为

84

。低年级生都得了同一个分数，高年级生平均分为

83

。每个低年级生得了多少分？

A teacher gave a test to a class in which

10\%

of the students are juniors and

90\%

are seniors. The average score on the test was

84.

The juniors all received the same score, and the average score of the seniors was

83.

What score did each of the juniors receive on the test?

85

88

93

94

98

取一个方便的班级人数，例如

10

名学生。

Take a convenient class size, such as

10

students

若有一名低年级生和九名高年级生，则

10\cdot 84 = 9\cdot 83 + s

。

With one junior and nine seniors,

10\cdot 84 = 9\cdot 83 + s

假设班上有

10

名学生：一名低年级生和九名高年级生。总分为

10\cdot 84=840

。

九名高年级生总分为

9\cdot 83=747

，所以低年级生的分数为

s=840-747=93

。

所以正确答案是 C。

Suppose the class has

10

students: one junior and nine seniors. The total of all scores is

10\cdot 84=840.

The nine seniors total

9\cdot 83=747,

so the junior’s score is

s=840-747=93.

Thus, the correct answer is C.

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