Difference between revisions of "2003 AMC 10B Problems/Problem 11"

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==Solution==
 
==Solution==
  
Using the point-slope formula, the equation of each line is
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Using the point-slope form, the equation of each line is
  
 
<cmath>y-15=3(x-10) \longrightarrow y=3x-15</cmath>
 
<cmath>y-15=3(x-10) \longrightarrow y=3x-15</cmath>

Revision as of 09:01, 6 July 2019

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 form, 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.

\[0=3x-15\longrightarrow x=5\] \[0=5x-35\longrightarrow x=7\] 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
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 AMC 10 Problems and Solutions

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