SOLUTION: A, B, C, and D are four points on a line such that AB : AC = 7 : 10 , and BD : CD = 9 : 2. If CD = 9 cm, what is the length of AB?

Question 1146038: A, B, C, and D are four points on a line such that AB : AC = 7 : 10 , and BD : CD = 9 : 2. If CD = 9 cm, what is the length of AB?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The statement of the problem is incomplete. The solution will be different, depending on the order of the four points.

To solve the problem, we have to assume a particular order of the four points. It is probable that the points A, B, C, and D are in that order; but the statement of the problem should specify that.

Assuming the order A-B-C-D, we can then find a solution as follows.

AB:AC = 7:10, so let AB = 7x and AC = 10x; that makes BC = 3x

BD:CD = 9:2, so let BD = 9y and CD = 2y; that makes BC = 7y

Then, CD = 9 and BC:CD = 7y:2y = 7:2 makes BC equal to (7/2)*9 = 31.5

And then BC = 31.5 and AB:BC = 7x:3x = 7:3 makes AB equal to (7/3)*31.5 = 73.5

ANSWER: AB = 73.5
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