Question

4 homework
question 31, 1.4.83
hw score: 93.75%, 30 of 32 points
points: 0 of 1
an investment group is renovating a commercial building and will rent offices to small businesses. the formula r = 2(s + 78) can be used to determine the monthly rent for an office with s square feet. all utilities are included in the monthly payment. for what square footage will the rent be less than $1200?
select the correct choice below and fill in the answer box to complete your choice.
(simplify your answer. type an integer or a decimal.)
a. the solution set is {s|s ≤ □ ft²}.
b. the solution set is {s|s < □ ft²}.
c. the solution set is {s|s ≥ □ ft²}.
d. the solution set is {s|s > □ ft²}.

Explanation:

Step1: Set up the inequality

We know that $R = 2(s + 78)$ and $R<1200$. So, we set up the inequality $2(s + 78)<1200$.

Step2: Divide both sides by 2

Dividing both sides of the inequality $2(s + 78)<1200$ by 2 gives $s + 78<\frac{1200}{2}$, which simplifies to $s + 78<600$.

Step3: Subtract 78 from both sides

Subtracting 78 from both sides of the inequality $s + 78<600$ gives $s<600 - 78$, so $s<522$.

Answer:

B. The solution set is $\{s|s < 522\mathrm{ft}^2\}$