In the base ten number system the number $526$ means $5 \times 10^2+2 \times 10 + 6$. 
In the Land of Mathesis, however, numbers are written in the base $r$. 
Jones purchases an automobile there for $440$ monetary units (abbreviated m.u). 
He gives the salesman a $1000$ m.u bill, and receives, in change, $340$ m.u. The base $r$ is:
$\textbf{(A)}\ 2\qquad \textbf{(B)}\ 5\qquad \textbf{(C)}\ 7\qquad \textbf{(D)}\ 8\qquad \textbf{(E)}\ 12$
If Jones received $340$ m.u. change after paying $1000$ m.u. for something that costs $440$ m.u., then
\[440_r + 340_r = 1000_r\]
This equation can be rewritten as
\[4r^2 + 4r + 3r^2 + 4r = r^3\]
Bring all of the terms to one side to get
\[r^3 - 7r^2 - 8r = 0\]
Factor to get
\[r(r-8)(r+1)=0\]
Since [base numbers](https://artofproblemsolving.com/wiki/index.php/Base_numbers) are always positive, base $r$ is $8$, which is answer choice $\boxed{\textbf{(D)}}$.