Points A, B, C, and D lie along a line, in that order. If AB:AC=1:5, and BC:CD=2:1, what is the ratio AB:CD?
A number or a short expression. Spacing and $ signs are ignored.
Solution
Suppose that AB=x for some x>0. Since AB:AC=1:5, then AC=5x. This means that BC=AC−AB=5x−x=4x. Since BC:CD=2:1 and BC=4x, then CD=2x. Therefore, AB:CD=x:2x=1:2.
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