Question

Write a system of inequalities. Then draw a graph that shows all of the possible dimensions of the dance floor.Two students disagree about how to solve a problem and have asked you for help. They have 220 ft. of ribbon to enclose a rectangular space in the gym for a dance floor. The dance floor has to be at least 70 ft. long to accommodate the anticipated number of dancers.

Answer 1

The system of inequalities for the dance floor dimensions are L ≥ 70 and 2L + 2W ≤ 220. To graph these inequalities, one should draw a coordinate plane with L as the horizontal axis and W as the vertical axis and mark the region that satisfies both inequalities.

Step-by-step explanation:

To define the possible dimensions for the dance floor using a system of inequalities, let L represent the length and W represent the width.

The first condition is that the length must be at least 70 feet. This gives us our first inequality:

• L ≥ 70

The second condition is set by the total amount of ribbon to enclose the rectangle, which means the perimeter must be at most 220 feet. Since the perimeter P of a rectangle is given by P = 2L + 2W, the second inequality is:

• 2L + 2W ≤ 220

To depict these constraints graphically, draw a coordinate plane with L on the horizontal axis and W on the vertical axis. The region that satisfies both inequalities is the feasible solution space for the dance floor dimensions.