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Problem 423

Algebra Difficulty 2.1 Find the answer CEMC Fermat

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 $AB:CD$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official 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, $AB:CD=x:2x=1:2$ .

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.