The average of three numbers $p$, $q$ and $r$ is $k$. $p$ is as much more than the average as $q$ is less…
The average of three numbers $p$, $q$ and $r$ is $k$. $p$ is as much more than the average as $q$ is less than the average. What is the value of $r$?
k
k - 1
k + 1
k/2
Solution
The average is $k$, so $p+q+r = 3k$. 'p is as much more than the average as q is less than the average' means $p - k = k - q$, i.e. $p + q = 2k$. Substituting: $2k + r = 3k$, so $r = k$.