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 Question from Florian: In Mr. Edgecomb's math class, 30 students took an exam on statistics. If the average passing grade was 84, the average failing grade was 60, and the overall average was 80, how many students passed the test?

Hi Florian,

Suppose the total of the grades of all 30 students was $T$ then the overall average would be $\large \frac{T}{30}.$ But you know the overall average was 80. Solve for $T.$

Suppose $n$ students passed the test and the total of their grades was $t.$ You know the average grade of the students who passed the test was 84. This gives you an equation in $n$ and $t.$

Since $n$ students passed the test, the number who didn't pass the test was $30 - n.$ The total of the grades of the students who didn't pass the test was $T - t.$ Their average was 60. This gives you a second equation in $n$ and $t.$

Solve for $n.$

Penny