Question

Jake is building a fence around his property. He wants the perimeter to be no more than 100 feet. He also wants the length to be at least 10 feet longer than the width. If he builds his fence according to these limits, which would be the maximum possible width of the fence?

A. 30 feet
B. 50 feet
C. 20 feet
D. 10 feet

Answer 1

C. 20 feet

Explanation:

Let x = width

Let y = length

If the length is at least 10 feet longer than the width:

⇒ x + 10 ≤ y

⇒ x ≤ y - 10

If the perimeter is to be no more than 100 ft:

⇒ 2x + 2y ≤ 100

⇒ x + y ≤ 50

⇒ x ≤ 50 - y

Equate the equations for x and solve for y:

⇒ y - 10 = 50 - y

⇒ 2y = 60

⇒ y = 30

Substitute found value of y into one of the inequalities for x:

⇒ x ≤ 30 - 10

⇒ x ≤ 20

Therefore, the maximum possible width of the fence is 20 feet.