2011 AMC 8 Problems/Problem 10: Difference between revisions

Revision as of 19:52, 20 January 2024

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

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)
Preceded by Problem 9	Followed by Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

@@ Line 15: / Line 15: @@
 ==Solution 2==
-Miles | Money | Remark
-    | 8     | 2 for tip
+\begin{array}{|c|c|c|}
+Miles & Money & Remark\\
-.5   | 5.6   | -2.4 for first 0.5 mi
+\hline
+& 8 & \text{2  for  tip} \\
-.3   | 0     | -5.6 for 2.8 mi
+\hline
+.5 & 5.6 & \text{-2.4  for  first  0.5  mi} \\
+\hline
+.3 & 0 & \text{-5.6  for  2.8  mi}
+\end{array}
 Miles travelled = <math>\boxed{\textbf{(C)}\ 3.3}</math>
-Can you format it properly.
+Solution by Anshulb, formatted by Cheetahboy93
-Thanks. --Anshulb
 ==Video Solution==

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