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

$\dfrac{s_1+\cdots+s_8}{8}=Q\implies s_1+\cdots+s_8=8Q$
$\dfrac{s_1+s_2+s_3}{3}=Z\implies s_1+s_2+s_3=3Z$

Substituting into the first equation, this means

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

Divide by 5 to get the average:

$\dfrac{s_4+\cdots+s_8}{5}=\dfrac{8Q-3Z}5$