1973 AHSME Problem 24

The check for a luncheon of 3 sandwiches, 7 cups of coffee and one piece of pie came to \$3.15. The check for a luncheon consisting of 4 sandwiches, 10 cups of coffee and one piece of pie came to \$4.20 at the same place. The cost of a luncheon consisting of one sandwich, one cup of coffee, and one piece of pie at the same place will come to

\textbf{(A)}\ 1.70 \qquad \textbf{(B)}\ 1.65 \qquad \textbf{(C)}\ 1.20 \qquad \textbf{(D)}\ 1.05 \qquad \textbf{(E)}\ 0.95$

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