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?

Answer 1

Answer:

x<20

Step-by-step explanation:

Answer 2

Building linear functions for each situation, the inequality is:

$18x + 100 < 15x + 160$

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Choice A:

• $18 per guest.
• $100 for renting.

Thus, the cost of inviting x guests is given by:

$C_a(x) = 18x + 100$

Choice B:

• $15 per guest.
• $160 for renting.

Thus, the cost of inviting x guests is given by:

$C_b(x) = 15x + 160$

A cost less than B, thus, the inequality is:

$C_a(x) < C_b(x)$

$18x + 100 < 15x + 160$

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