Andrew is creating a rectangular dog run in his back yard. The length of the dog run is 20 feet. The perimeter of the dog run must be at least 48 feet and no more than 80 feet. Use a compound inequality to find the range of values for the width of the dog run.

Step-by-step explanation:

Perimiter = distance around. In this case the sum of the lengths and breadths of the dog run.

let a = length and b = breadth

2a + 2b ≥ 48

2a + 2b ≤ 80

since a = 20, we substitute for a in both equations

2 (20) + 2b ≥ 48

40 + 2b ≥ 48

2b ≥ 48 - 40

2b ≥ 8

b ≥ 4

In the second equation, we have;

2 (20) + 2b ≤ 80

40 + 2b ≤ 80

2b ≤ 80 - 40

2b ≤ 40

b ≤ 20

So the width must be between 4ft and 20ft for the dog run to be within the requisite criteria