CEMC Fermat, 2019

Algebra Difficulty 1.1 Junior Find the answer Canada

In the diagram, point $P$ is on the number line at 3 and $V$ is at 33. The number line between $3$ and $33$ is divided into six equal parts by the points $Q,R,S,T,U$ .

What is the sum of the lengths of $PS$ and $TV$ ?

Pick one

Solution

The segment of the number line between 3 and 33 has length $33-3=30$ .

Since this segment is divided into six equal parts, then each part has length $30 \div 6 = 5$ .

The segment $PS$ is made up of 3 of these equal parts, and so has length $3 \times 5 = 15$ .

The segment $TV$ is made up of 2 of these equal parts, and so has length $2 \times 5 = 10$ .

Thus, the sum of the lengths of $PS$ and $TV$ is $15+10$ or $25$ .

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