2018 AMC 12B Problem 3

Below is the professionally curated solution for Problem 3 of the 2018 AMC 12B, 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 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:linear equationslopecoordinate geometry

Difficulty rating: 1240

3.

A line with slope 22 intersects a line with slope 66 at the point (40,30).(40, 30). What is the distance between the xx-intercepts of these two lines?

55

1010

2020

2525

5050

Solution:

The line of slope 22 is y30=2(x40);y-30=2(x-40); setting y=0y=0 gives x=25.x=25. The line of slope 66 is y30=6(x40);y-30=6(x-40); setting y=0y=0 gives x=35.x=35.

The distance between the intercepts is 3525=10.|35-25|=10.

Thus, the correct answer is B.

Problem 3 in Other Years