AMC8 2011

AMC8 2011 · Q10

AMC8 2011 · Q10. It mainly tests Linear equations, Rates (speed).

The taxi fare in Gotham City is $2.40 for the first 1/2 mile and additional mileage charged at the rate $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10?

哥谭市的出租车费，第一半英里2.40美元，此后每额外0.1英里0.20美元。你计划给司机2美元小费。用10美元能乘坐多少英里？

(A) 3.0 3.0

(B) 3.25 3.25

(D) 3.5 3.5

(E) 3.75 3.75

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let $x$ be the number of miles you ride. The number of miles you ride after the first half mile is $x-0.5.$ We can write this equation: \begin{align*} 10 &= 2.4 + 0.2 \times \frac{x-0.5}{0.1} + 2\\ 5.6 &= 2(x-0.5)\\ 2.8 &= x-0.5\\ x &= \boxed{\textbf{(C)}\ 3.3}\end{align*}

设$x$为乘坐的英里数。超过第一半英里后的英里数为$x-0.5$。我们可以写出这个方程： \begin{align*} 10 &= 2.4 + 0.2 \times \frac{x-0.5}{0.1} + 2\\ 5.6 &= 2(x-0.5)\\ 2.8 &= x-0.5\\ x &= \boxed{\textbf{(C)}\ 3.3}\end{align*}

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