In Professor Tuffguy's mathematics class, 36 students took the final exam. If the average passing grade was 78, the average failing grade was 60, and the class average was 71, how many of these 36 student passed the final?

Answer 1

If x passed, then the rest (36-x) failed. So, adding up all the grades, we have

78x + 60(36-x) = 71*36

This is just a mixture problem in other guise.