In Mr. Patterson's class, the average score among students who studied for an exam was 78. The average among students who did not study was 54. The overall class average was 70. What portion of the class did not study? Express your answer as a common fraction.

Answer 1

Let x be the portion of the class that did not study.

Therefore, the portion of the class that studied is 1 - x.

The average score among students who studied can be represented as 78(1-x) and the average score among students who did not study can be represented as 54x.

The overall class average can be represented as (78(1-x) + 54x)/2 = 70.

Solving the equation gives us:
(78 - 78x + 54x)/2 = 70
(78 + 24x)/2 = 70
78 + 24x = 140
24x = 62
x = 62/24
x = 31/12

Therefore, the portion of the class that did not study is 31/12.