Let f be the area of an ice rink in square feet, and p the price in dollars. The area of an ice rink has to be at least 1000 square feet and at most 17 000 square feet. We can write an inequality to represent this information.
1000 ≤ f ≤ 17 000
We also know that the price ranges from as little as $ 10 000 to as much as $ 150 000.
10 000 ≤ p ≤ 150 000
If we combine the inequalities, we get a system of inequalities.
1000 ≤ f ≤ 17 000 10 000 ≤ p ≤ 150 000
Graphing the System
The area of an ice rink f is the independent variable and the price p is the dependent variable. The solution set contains points which are between the vertical lines f=1000 and f=17 000 and between the horizontal lines p=10 000 and p=150 000. The solution to this system of inequalities is where the shadings overlap.
1cm Ice Rink Resurfacers
b To name one possible solution we need any point from the overlapping area. We will plot the point on the graph and name it.
1cm Ice Rink Resurfacers
One possible solution is (10 000,80 000). In this situation, this means an ice resurfacer for a rink of 10 000 square feet and a price of $80 000.
c To check whether (15 000,30 000) is a solution, let's plot it in the coordinate plane and see if it lies in the overlapping area.
As can be seen in the graph, the point (15 000,30 000) is a solution to this system of inequalities.
