2018 AMC 12B Problem 3 — Solution | LIVE by Po-Shen Loh

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2018 AMC 12B Problem 3

Attempt Problem 3 of the 2018 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

3.

A line with slope $2$ intersects a line with slope $6$ at the point $(40, 30).$ What is the distance between the $x$ -intercepts of these two lines?

$5$

$10$

$20$

$25$

$50$

Answer: B

Concepts:linear equation slope coordinate geometry

Difficulty rating: 1240

Solution:

The line of slope $2$ is $y-30=2(x-40);$ setting $y=0$ gives $x=25.$ The line of slope $6$ is $y-30=6(x-40);$ setting $y=0$ gives $x=35.$

The distance between the intercepts is $|35-25|=10.$

Thus, the correct answer is B.

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