2012 AMC 10B 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

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

Show solution

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{aligned}x+0.1x+0.15x&=1.25x\\&=27.5\end{aligned}

Therefore,

x=22.

Thus, the correct answer is D .

Tagged: percentage · linear equation