Question

The average of 8 scores is Q. If the average of 3 of the scores is Z, what is the average of the other 5 scores?

Answer 1

`(s_1+\cdots+s_8)/(8)=Q\implies s_1+\cdots+s_8=8Q`

`(s_1+s_2+s_3)/(3)=Z\implies s_1+s_2+s_3=3Z`

Substituting into the first equation, this means


`s_4+\cdots+s_8=8Q-3Z`

Divide by 5 to get the average:


`(s_4+\cdots+s_8)/(5)=\frac{8Q-3Z}5`