2012 AMC 10B 第 5 题

Question

Anna 在华盛顿特区一家餐馆用餐，餐费销售税为

10\%

。她按税前餐费留下

15\%

的小费，税也按小费前的餐费计算。她晚餐总共花了

\$27.50

。她不含税和小费的餐费是多少美元？

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

税和小费都是税前餐费的百分比。

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

总账单是餐费的

125\%

。

The total bill is

125\%

of the meal price

设税前餐费为

x

。税为

0.1x

，小费为

0.15x

。总花费满足

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

所以

x=22

。

所以正确答案是 D。

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 .

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