John's class had an average score of 75.
Amy's class had an average score of 78.
Both classes together had an average of 77.
Find the ratio of the number of students in John's class to Amy's class.
Ok so...
If John was the only person in his class and Amy was the only person in her class, the average of both classes would be 76.5.
Therefore, there must be more people in Amy's class than in John's class.
I will guess and check.
If the scores of both classes put together were 75, 78, 78, then the average of both classes would be (75+77+78)/3=76.5
Testing larger, equivalent ratios to 1/2 finds that this continues to hold true.
So the answer is 1 student in John's class for every 2 student's in Amy's class.
Is there an easier way to do this?