Difference between revisions of "2004 AMC 8 Problems/Problem 1"

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== Problem ==
 
== Problem ==
Ona map, a <math>12</math>-centimeter length represents <math>72</math> kilometers. How many kilometers does a <math>17</math>-centimeter length represent?
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On a map, a <math>12</math>-centimeter length represents <math>72</math> kilometers. How many kilometers does a <math>17</math>-centimeter length represent?
  
 
<math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 102\qquad\textbf{(C)}\ 204\qquad\textbf{(D)}\ 864\qquad\textbf{(E)}\ 1224 </math>
 
<math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 102\qquad\textbf{(C)}\ 204\qquad\textbf{(D)}\ 864\qquad\textbf{(E)}\ 1224 </math>
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== Solution ==
 
== Solution ==
 
We set up the proportion  <math>\frac{12  \text{cm}}{72  \text{km}}=\frac{17 \text{cm}}{x \text{km}}</math>. Thus <math>x=102 \Rightarrow \boxed{\textbf{(B)}\ 102}</math>
 
We set up the proportion  <math>\frac{12  \text{cm}}{72  \text{km}}=\frac{17 \text{cm}}{x \text{km}}</math>. Thus <math>x=102 \Rightarrow \boxed{\textbf{(B)}\ 102}</math>
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== Solution 2 ==
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Since we know <math>12</math> centimeters on the map is equal to <math>72</math> kilometers, <math>1</math> centimeter on the map is simply <math>72/12</math>, which is <math>6</math>. The problem is asking how many kilometers a <math>17</math>-centimeter length represents, so we multiply <math>6</math> by <math>17</math> which is simply 102, your answer.
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==See Also==
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{{AMC8 box|year=2004|before=First <br />Question|num-a=2}}
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{{MAA Notice}}

Latest revision as of 04:21, 24 July 2018

Problem

On a map, a $12$-centimeter length represents $72$ kilometers. How many kilometers does a $17$-centimeter length represent?

$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 102\qquad\textbf{(C)}\ 204\qquad\textbf{(D)}\ 864\qquad\textbf{(E)}\ 1224$

Solution

We set up the proportion $\frac{12  \text{cm}}{72  \text{km}}=\frac{17 \text{cm}}{x \text{km}}$. Thus $x=102 \Rightarrow \boxed{\textbf{(B)}\ 102}$

Solution 2

Since we know $12$ centimeters on the map is equal to $72$ kilometers, $1$ centimeter on the map is simply $72/12$, which is $6$. The problem is asking how many kilometers a $17$-centimeter length represents, so we multiply $6$ by $17$ which is simply 102, your answer.

See Also

2004 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
First
Question
Followed by
Problem 2
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All AJHSME/AMC 8 Problems and Solutions

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