Points A, B and C are collinear. Point B is between Point A and Point C. Find the length of BC if BC=3x-2, AB=12, and AC=5x+2.

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20-08-2014
Mathematics

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Points A, B and C are collinear. Point B is between Point A and Point C. Find the length of BC if BC=3x-2, AB=12, and AC=5x+2.

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iceyinyeung iceyinyeung · Answer 1 · 2014-08-21T03:01:55-04:00

iceyinyeung iceyinyeung

21-08-2014

A very simple drawing of this problem would be something like
A---B-------C
B is somewhere in the middle, we don't know yet. But a simple fact that you can get out of the picture is that AC - BC = AB, or
(5x+2) - (3x-2) = 12. Solve:
2x + 4 = 12
2x = 8
x = 4
Plug in x=4 for BC:
3x-2 =
3(4) - 2 =
12 - 2 =
10
BC is therefore 10 units long.

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