2011 AMC 8 Problems/Problem 10

Problem

The taxi fare in Gotham City is $2.40 for the first $\frac12$ 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?

$\textbf{(A) }3.0\qquad\textbf{(B) }3.25\qquad\textbf{(C) }3.3\qquad\textbf{(D) }3.5\qquad\textbf{(E) }3.75$

Solution 1

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:

$\begin{align*} 10 &= 2.4 + 0.2 \times \frac{x-0.5}{0.1} + 2\\ 5.6 &= 2(x-0.5)\\ 2.8 &= x-0.5\\ x &= \boxed{\textbf{(C)}\ 3.3}\end{align*}$

Solution 2

\begin{array}{|c|c|c|} Miles & Money & Remark\\ \hline 0 & 8 & \text{2 for tip} \\ \hline 0.5 & 5.6 & \text{-2.4 for first 0.5 mi} \\ \hline 3.3 & 0 & \text{-5.6 for 2.8 mi} \end{array}

Miles travelled = $\boxed{\textbf{(C)}\ 3.3}$

Solution by Anshulb, formatted by Cheetahboy93

Video Solution

https://youtu.be/2TYKNdpOvok

~savannahsolver

2011 AMC 8 (Problems • Answer Key • Resources)
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All AJHSME/AMC 8 Problems and Solutions

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2011 AMC 8 Problems/Problem 10

Contents

Problem

Solution 1

Solution 2

Video Solution

See Also