In a number line, point is at 3 and is at 33. The number line between 3 and 33 is divided into six equal parts by the points . What is the sum of the lengths of and ?
Solution
The segment of the number line between 3 and 33 has length . Since this segment is divided into six equal parts, then each part has length . The segment is made up of 3 of these equal parts, and so has length . The segment is made up of 2 of these equal parts, and so has length . Thus, the sum of the lengths of and is or 25.
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