2003 AMC 10B Problems/Problem 11

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Problem

A line with slope $3$ intersects a line with slope $5$ at point $(10,15)$. What is the distance between the $x$-intercepts of these two lines?

$\textbf{(A) } 2 \qquad\textbf{(B) } 5 \qquad\textbf{(C) } 7 \qquad\textbf{(D) } 12 \qquad\textbf{(E) } 20$

Solution

Using the point-slope formula, the equation of each line is

\[y-15=3(x-10) \longrightarrow y=3x-15\\ y-15=5(x-10) \longrightarrow y=5x-35\]

Substitute in $y=0$ to find the $x$-intercepts.

\[0=3x-15\longrightarrowx=5
0=5x-35\longrightarrowx=7\] (Error compiling LaTeX. Unknown error_msg)

The difference between them is $7-5=\boxed{\textbf{(A) \ } 2}$.

See Also

2003 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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All AMC 10 Problems and Solutions