2013 Gauss 8 Problem 20

Christina and Frieda want to buy the same book. Christina has \frac{3}{4} of the money needed to buy the book and Frieda has half of the money needed to buy the book. If the book was \$3 cheaper, then together they would have exactly enough money to buy 2 copies of the book. What is the original price of the book?

\textbf{(A)}\ \$4\quad \textbf{(B)}\ \$16\quad \textbf{(C)}\ \$12\quad \textbf{(D)}\ \$10\quad \textbf{(E)}\ \$8

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.