Maths Olympiad Prep

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Algebra Difficulty 1.4 Junior Find the answer Canada

In the graph, the five points show the money earned versus time
worked for each of five employees. Each was paid a different but fixed
number of dollars per hour. Which letter represents the employee who was
paid the most money per hour?

Figure 0

Figure for this problem

Pick one

Solution

The vertical axis represents money earned (in dollars) and the
horizontal axis represents time (in hours).

Thus, each employee’s money earned per hour is the slope of the line
segment from the origin (0,0)(0,0) to
the employee’s letter.

Figure 1

The employee who was paid the most money per hour is the employee
whose line segment has the greatest slope.

The line segment with the greatest slope is the steepest of the 55 line segments, and so Employee AA was paid the most money per hour.

Alternately, we could add numbers to each of the axes and use them to
determine the slope of each line, and thus the money earned per hour for
each employee.

Figure for this problem

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