Question

the warbler house inn offers two plans for wedding parties. under plan a, the inn charges $35 for each person in attendance. under plan b, the inn charges $1500 plus $25 for each person in excess of the first 35 who attend. for what size parties will plan b cost less? (assume that more than 35 guests will attend.) let p represents the number of guests. select the correct choice below and fill in the answer box to complete your choice. (round to the nearest whole number.) a. the solution set is {p | p ≤ }. b. the solution set is {p | p < }. c. the solution set is {p | p > }. d. the solution set is {p | p ≥ }.

Explanation:

Step1: Set up cost - functions

Let $p$ be the number of guests ($p>35$). The cost of plan A, $C_A = 35p$. The cost of plan B, $C_B=1500 + 25(p - 35)$.

Step2: Expand the cost - function of plan B

$C_B=1500+25p-875=25p + 625$.

Step3: Set up the inequality

We want to find when $C_B

Step4: Solve the inequality

Subtract $25p$ from both sides: $625<35p - 25p$, which simplifies to $625 < 10p$. Then divide both sides by 10: $p>\frac{625}{10}=62.5$.

Step5: Round to the nearest whole number

Since $p$ represents the number of people and we need $p>62.5$, rounding up to the nearest whole number, we get $p > 63$.

Answer:

C. The solution set is $\{p\mid p > 63\}$