1998 Gauss 8 Problem 25

A sum of money is to be divided among Allan, Bill and Carol. Allan receives \$1 plus one-third of what is left. Bill then receives \$6 plus one-third of what remains. Carol receives the rest, which amounts to \$40. How much did Bill receive?

\textbf{(A)}\ \$26\quad \textbf{(B)}\ \$28\quad \textbf{(C)}\ \$30\quad \textbf{(D)}\ \$32\quad \textbf{(E)}\ \$34

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.