Difference between revisions of "2011 AMC 8 Problems/Problem 10"

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==Problem==
 
The taxi fare in Gotham City is <nowiki>$2.40</nowiki> for the first <math>\frac12</math> mile and additional mileage charged at the rate <nowiki>$0.20</nowiki> for each additional 0.1 mile. You plan to give the driver a <nowiki>$2</nowiki> tip. How many miles can you ride for <nowiki>$10</nowiki>?
 
The taxi fare in Gotham City is <nowiki>$2.40</nowiki> for the first <math>\frac12</math> mile and additional mileage charged at the rate <nowiki>$0.20</nowiki> for each additional 0.1 mile. You plan to give the driver a <nowiki>$2</nowiki> tip. How many miles can you ride for <nowiki>$10</nowiki>?
  
 
<math> \textbf{(A) }3.0\qquad\textbf{(B) }3.25\qquad\textbf{(C) }3.3\qquad\textbf{(D) }3.5\qquad\textbf{(E) }3.75 </math>
 
<math> \textbf{(A) }3.0\qquad\textbf{(B) }3.25\qquad\textbf{(C) }3.3\qquad\textbf{(D) }3.5\qquad\textbf{(E) }3.75 </math>
  
==Solution==
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==Solution 1 (Algebra)==
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Let <math>x</math> be the number of miles you ride. The number of miles you ride after the first half mile is <math>x-0.5.</math> We can write this equation:
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<cmath>\begin{align*} 10 &= 2.4 + 0.2 \times \frac{x-0.5}{0.1} + 2\\
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5.6 &= 2(x-0.5)\\
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2.8 &= x-0.5\\
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x &= \boxed{\textbf{(C)}\ 3.3}\end{align*}</cmath>
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==Solution 2 (Table)==
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\begin{array}{|c|c|c|}
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Miles & Money & Remark\\
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\hline
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0 & 8 & \text{2  for  tip} \\
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\hline
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0.5 & 5.6 & \text{-2.4  for  first  0.5  mi} \\
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\hline
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3.3 & 0 & \text{-5.6  for  2.8  mi}
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\end{array}
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Miles travelled = <math>\boxed{\textbf{(C)}\ 3.3}</math>
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Solution by Anshulb, formatted by Cheetahboy93
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==Video Solution==
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https://youtu.be/2TYKNdpOvok
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~savannahsolver
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2011|num-b=9|num-a=11}}
 
{{AMC8 box|year=2011|num-b=9|num-a=11}}
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{{MAA Notice}}

Latest revision as of 23:20, 18 February 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 1 (Algebra)

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 (Table)

\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

See Also

2011 AMC 8 (ProblemsAnswer KeyResources)
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

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