2007 AMC 10B Problem 16

Question

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

Take a convenient class size, such as

10

students

With one junior and nine seniors,

10\cdot 84 = 9\cdot 83 + s

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.

Problem 16 in other years