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Algebra Difficulty 1.9 Junior Find the answer

In a number line, point PP is at 3 and VV is at 33. The number line between 3 and 33 is divided into six equal parts by the points Q,R,S,T,UQ, R, S, T, U. What is the sum of the lengths of PSPS and TVTV?

A number or a short expression. Spacing and $ signs are ignored.

Solution

The segment of the number line between 3 and 33 has length 333=3033 - 3 = 30. Since this segment is divided into six equal parts, then each part has length 30÷6=530 \div 6 = 5. The segment PSPS is made up of 3 of these equal parts, and so has length 3×5=153 \times 5 = 15. The segment TVTV is made up of 2 of these equal parts, and so has length 2×5=102 \times 5 = 10. Thus, the sum of the lengths of PSPS and TVTV is 15+1015 + 10 or 25.

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