Problem:
All students at Adams High School and at Baker High School take a certain exam. The average scores for boys, for girls, and for boys and girls combined, at Adams HS and Baker HS are shown in the table, as is the average for boys at the two schools combined. What is the average score for the girls at the two schools combined?
Answer Choices:
A.
B.
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D.
E.
Solution:
We want a weighted average, , of and , with weights proportional to the number of girls at Adams HS and Baker HS, respectively. We obtain these weights as follows: Let
number of boys at Adams, number of boys at Baker,
number of girls at Adams, number of girls at Baker.
Then, from the first column of the table we obtain , whict leads to . Similarly, the second column shows that and the first row shows that . Thus