1997 AHSME Problem 22

Ashley, Betty, Carlos, Dick, and Elgin went shopping. Each had a whole number of dollars to spend, and together they had 56 dollars. The absolute difference between the amounts Ashley and Betty had to spend was 19 dollars. The absolute difference between the amounts Betty and Carlos had was 7 dollars, between Carlos and Dick was 5 dollars, between Dick and Elgin was 4 dollars, and between Elgin and Ashley was 11 dollars. How many dollars did Elgin have?

\textbf{(A)}\ 6\qquad\textbf{(B)}\ 7\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 10

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.