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. this situation is modeled by the compound inequality 100 ≤ ≤ 200. (use integers or decimals for any numbers in the expression. do not include the $ symbol in your answer.)

Explanation:

Step1: Set up the cost - length relationship

Let the length of the fencing be $l$. The cost of the fencing is $C = 2.5l$. We know that $100\leq C\leq200$. Substituting $C = 2.5l$ into the compound - inequality, we get $100\leq2.5l\leq200$.

Step2: Solve the left - hand side of the inequality

To solve $100\leq2.5l$, divide both sides by 2.5. $\frac{100}{2.5}\leq\frac{2.5l}{2.5}$, which simplifies to $40\leq l$.

Step3: Solve the right - hand side of the inequality

To solve $2.5l\leq200$, divide both sides by 2.5. $\frac{2.5l}{2.5}\leq\frac{200}{2.5}$, which simplifies to $l\leq80$.

Answer:

$40\leq l\leq80$