Question

lisa is planning for a party. she receives quotes from two party planners. choice a quotes $18 per guest, plus $100 for renting the party hall. choice b quotes $15 per guest, plus $160 for renting the party hall. which inequality represents the number of guests lisa can invite, if choice a were to cost less than choice b? a. x > 20 b. x < 30 c. x > 30 d. x < 20

Explanation:

Step1: Set up cost - functions

Let \(x\) be the number of guests. The cost of choice A, \(C_A=18x + 100\). The cost of choice B, \(C_B=15x+160\).

Step2: Set up the inequality

We want to find when \(C_A

Step3: Solve the inequality

Subtract \(15x\) from both sides: \(18x-15x + 100<15x-15x + 160\), which simplifies to \(3x+100<160\). Then subtract 100 from both sides: \(3x+100 - 100<160 - 100\), getting \(3x<60\). Divide both sides by 3: \(x < 20\).

Answer:

D. \(x < 20\)