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

Answer
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
× = possible number of square feet

Minimum spending = $100
Maximum spending = $200
Cost per square feet = $2.50
let
× = possible number of square feet
The inequality:
100 ≤ 2.50× ≥ 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 < 2.50× ≥ 200
divide the inequality into 2
100 < 2.50x
× ≤ 100/2.5
× ≤40
the other part:
2.50x ≥ 200
× ≥ 200/2.50
× ≥ 80
Therefore,
the possible length of the dog leash is 80

Answer 2

20 ≤ L + W ≤ 40

Explanation:

[answer is marked by ** symbol]

The perimeter (P) of a rectangle is given by the formula:

P = 2L + 2W

In this case, you want to spend between $100 and $200 on fencing, and the cost is $2.50 per foot. So, you can write the cost equation as:

Cost = 2.50 (2L + 2W)

Now, you want the cost to be between $100 and $200, which leads to a compound inequality:

$100 ≤ 2.50 (2L + 2W) ≤ $200

Now, divide each part of the compound inequality by 2.50 to isolate the expression (2L + 2W):

$100 / 2.50 ≤ 2L + 2W ≤ $200 / 2.50

40 ≤ 2L + 2W ≤ 80

Now, divide each part by 2 to find L + W:

**20 ≤ L + W ≤ 40

**This compound inequality models the possible length of the dog run. It states that the length plus the width of the dog run must be between 20 feet and 40 feet to stay within the budget of $100 to $200 for fencing.