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Problem 425

AMC 12 late, AIME early

Geometry Difficulty 4.8 Find the answer

On a straight line, ten points were placed at equal intervals, and they occupied a segment of length $a$ . On another straight line, one hundred points were placed at the same intervals, and they occupied a segment of length $b$ . How many times is $b$ greater than $a$ ?

Your answer

Official solution

On a segment of length $a$ , 9 intervals fit, and on a segment of length $b-99$ . Therefore, $b=11a$ .

11 times.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.