2012 AMC 10B Problems/Problem 5

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Problem 5

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?

$\textbf{(A)}\ 18\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 21\qquad\textbf{(D)}\ 22\qquad\textbf{(E)}\ 24$


Solutions

Let X be the cost of her dinner.

$27.50=X+\frac{1}{10}*X+\frac{3}{20}*X$

$27+\frac{1}{2}=\frac{5}{4}*X$

$\frac{55}{2}=\frac{5}{4}X$

$\frac{55}{2}*\frac{4}{5}=X$

$\boxed{22=X}$

OR

$\textbf{(D)}$

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