Library / /35 of 310

, 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 $25$ .

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.