Anna enjoys dinner at a restaurant in Washington, D.C., where the sales tax on meals is 10%. She leaves a 15% tip on the price of her meal before the sales tax is added, and the tax is calculated on the pre-tip amount. She spends a total of 27.50 dollars for dinner. What is the cost of her dinner without tax or tip in dollars?
$\textbf{(A)}\ 18\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 21\qquad\textbf{(D)}\ 22\qquad\textbf{(E)}\ 24$
Let $x$ be the cost of her dinner. 
$27.50=x+\frac{1}{10}*x+\frac{3}{20}*x$
$27+\frac{1}{2}=\frac{5}{4}*x$
$\frac{55}{2}=\frac{5}{4}x$
$\frac{55}{2}*\frac{4}{5}=x$
$x=22$
$\boxed{\textbf{(D)}}$