2003 AMC 10B Problem 11 — Solution | LIVE by Po-Shen Loh

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2003 AMC 10B Problem 11

Below is the professionally curated solution for Problem 11 of the 2003 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 10B solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:coordinate geometry slope linear equation

Difficulty rating: 1240

11.

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

$2$

$5$

$7$

$12$

$20$

Solution:

The lines are $y-15=3(x-10)$ and $y-15=5(x-10).$

Setting $y=0$ gives $x$ -intercepts $x=5$ and $x=7.$ The distance between $(5,0)$ and $(7,0)$ is $2.$

Thus, the correct answer is A.

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