SOLUTION: Two classes took a test. Class A averaged 80 and class B averaged 90. The two classes together averaged about 83. Which class has more students?

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Question 357818: Two classes took a test. Class A averaged 80 and class B averaged 90. The two
classes together averaged about 83. Which class has more students?

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = # students in class A, b = # students in class B.
Sum of all scores in Class A = 80a,
Sum of all scores in Class B = 90b.
By the given, %2880a+%2B+90b%29%2F%28a%2Bb%29+=+83,
so 80a+%2B+90b+=+83a+%2B+83b, or
7b+=+3a,
b+=+%283a%29%2F7.
Since a number between 0 and 1 has to be multiplied to a to equal b, then a>b.
Therefore class A has more students.