Question

chris can be paid in one of two ways. plan a is a salary of $480 per month, plus a commission of 8% of gross sales. plan b is a salary of $825 per month, plus a commission of 3% of gross sales. for what amount of gross sales should chris select plan a? let s represent the amount of gross sales in dollars. 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≤ }. b. the solution set is {s | s< }. c. the solution set is {s | s≥ }. d. the solution set is {s | s> }.

Explanation:

Step1: Set up equations for each plan

Let $s$ be the amount of gross - sales.
The total pay for Plan A is $P_A = 480+0.08s$.
The total pay for Plan B is $P_B = 825 + 0.03s$.

Step2: Set up the inequality for when Plan A is better

We want to find when $P_A>P_B$.
So, $480 + 0.08s>825+0.03s$.

Step3: Solve the inequality

Subtract $0.03s$ from both sides:
$480+0.08s - 0.03s>825+0.03s - 0.03s$.
$480 + 0.05s>825$.
Subtract 480 from both sides:
$0.05s>825 - 480$.
$0.05s>345$.
Divide both sides by 0.05:
$s>\frac{345}{0.05}$.
$s > 6900$.

Answer:

D. The solution set is $\{s|s > 6900\}$