2012 AMC 10B Problem 5

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

Tax and tip are both percentages of the pre-tax meal price

The total bill is

125\%

of the meal price

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 .

Problem 5 in other years