Question

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 $\$27.50$ for dinner. What is the cost of her dinner without tax or tip?

$\$18$

$\$20$

$\$21$

$\$22$

$\$24$

Answer: D

Concepts:percentage linear equation

Difficulty rating: 900

Solution:

Suppose the original price is $x.$ Then, the tax is $0.1x$ and the tip is $0.15x.$ This makes the total payment equal to: $\begin{align*}x+0.1x+0.15x&=1.25x\\&=27.5\end{align*}$ Therefore, $x=22.$

Thus, the correct answer is D .

2012 AMC 10B Problem 5

Answer: D

Difficulty rating: 900

Solution:

Problem 5 in Other Years