Question

a medical insurance company offers two prescription - drug insurance plans. with plan 1, james would pay the first $150 of his prescription costs and 30% of all after that. with plan 2, james would pay the first $280 of costs, but only 10% of the rest. for what amount of prescription costs will plan 2 save james money? (assume that his prescription costs exceed $280.) let c represent the cost of prescriptions. select the correct choice below and fill in the answer box to complete your choices. (simplify your answer. round to the nearest integer as needed.) a. the solution set is {c|c > }. b. the solution set is {c|c ≤ }. c. the solution set is {c|c < }. d. the solution set is {c|c ≥ }.

Explanation:

Step1: Set up cost - functions for each plan

Let $c$ be the cost of prescriptions. For plan 1, the cost $y_1$ that James pays is $y_1 = 150+0.3(c - 150)$ since he pays the first $\$150$ and 30% of the amount above $\$150$. For plan 2, the cost $y_2$ that James pays is $y_2=280 + 0.1(c - 280)$ since he pays the first $\$280$ and 10% of the amount above $\$280$.

Step2: Set up the inequality

We want to find when plan 2 saves James money, so we set up the inequality $y_2\[

$$\begin{align*} 280+0.1(c - 280)&<150+0.3(c - 150)\\ 280 + 0.1c-28&<150+0.3c - 45\\ 252+0.1c&<105 + 0.3c\\ 252-105&<0.3c-0.1c\\ 147&<0.2c\\ c&>\frac{147}{0.2}=735 \end{align*}$$

\]

Answer:

A. The solution set is $\{c|c > 735\}$