2004 AMC 8 Problems/Problem 1

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)
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All AJHSME/AMC 8 Problems and Solutions

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