Compound Inequality

Question

​The length of a rectangle is 20 meters longer than the width. The perimeter must be between 80 and 100 meters. Write and solve a compound inequality to determine the possible values for the width of the rectangle.

Answer 1

80 ≤ p ≤ 100

p = 2l + 2w

l = w + 20

p = 2(w + 20) + 2w

p = 2w + 40 + 2w

p = 4w + 40

80 ≤ p ≤ 100

80 ≤ 4w + 40 ≤ 100

or,

40 ≤ 4w ≤ 60

or,

10 ≤ w ≤ 15