2012 AMC 10B Problems/Problem 5

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.

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

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

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

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

$x=22$

$\boxed{\textbf{(D)}}$

2012 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

2012 AMC 10B Problems/Problem 5

Problem 5

Solutions

See Also