Question

Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft. Write and solve a compound inequality to model the possible length of the dog run. ​

Answer 1

Write and solve a compound inequality to model the possible length of the dog run.

The inequality to model the possible length of the dog run is;. 100 ≤ 2.50x ≥ 200

And the possible length of the dog run is 80ft.

Minimum spending = $100

Maximum spending = $200

Cost per square feet = $2.50

let

x = possible number of square feet

The inequality:

100 ≤ 2.50x ≥ 200

This means possible number of square feet constructed is greater than or equal to $100 or less than or equal to $200

solve:

100 ≤ 2.50x ≥ 200

divide the inequality into 2

100 ≤ 2.50x

x ≤ 100/2.5

x ≤ 40

the other part:

2.50x ≥ 200

x ≥ 200/2.50

x ≥ 80

Therefore,

the possible length of the dog run is 80 feet

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