The mean of three numbers is $10$ more than the least of the numbers and $15$
less than the greatest. The median of the three numbers is $5$. What is their
sum?
$\textbf{(A)}\ 5\qquad \textbf{(B)}\ 20\qquad \textbf{(C)}\ 25\qquad \textbf{(D)}\ 30\qquad \textbf{(E)}\ 36$
Let $m$ be the mean of the three numbers. Then the least of the numbers is $m-10$
and the greatest is $m + 15$. The middle of the three numbers is the median, $5$. So
$\dfrac{1}{3}[(m-10) + 5 + (m + 15)] = m$, which can be solved to get $m=10$.
Hence, the sum of the three numbers is $3\cdot 10 = \boxed{\textbf{(D) }30}$.