A large engineering firm offers its employees paid time off to volunteer in the community, with a company goal of more than 150 volunteer hours per week. Employees can sign up for a shorter 2-hour volunteer slot or a longer 3-hour volunteer slot each week.
Which graph represents how many shorter slots, x, and longer slots, y, the company needs to fill each week?
Since the company goal is more than 150 volunteer hours per week, the total number of volunteer slots required each week is greater than 150 / 2 (since a shorter slot is 2 hours long) or 75 slots, and 150 / 3 (since a longer slot is 3 hours long) or 50 slots. Thus, the company needs to fill more shorter slots than longer slots each week.
A possible representation of the number of shorter slots, x, and longer slots, y, the company needs to fill each week could be:
y = 50
x > 75
This can be graphed on a coordinate plane where the x-axis represents the number of shorter slots and the y-axis represents the number of longer slots. The graph would have a vertical line at x = 75 representing the minimum number of shorter slots needed and a horizontal line at y = 50 representing the number of longer slots needed. The area above the vertical line and to the right of the horizontal line would represent all the possible combinations of shorter and longer slots that would meet the company's goal of more than 150 volunteer hours per week.