A graph between number of guests and prices. The x-axis represents guests and ranges from 0 to 50 in increments of 10. The y-axis represents price and ranges from 0 to 300 in increments of 25.

Question

Rafael is trying to book a graduation party. The party pavilion charges $100 for the first 10 people, $150 for more than 10 and up to 20 people, $200 for more than 20 and up to 30 people, $250 for more than 30 and up to 40 people, and $275 for more than 40 and up to 50 people. If Rafael wants to spend $250 for this party, how many people can he invite?

(1 point)
Responses

30<x≤40
30 less than x less-than-or-equal-to 40

20<x≤30
20 less than x less-than-or-equal-to 30

30<x≤50
30 less than x less-than-or-equal-to 50

20<x≤40

Answer 1

To determine how many guests Rafael can invite if he wants to spend $250 for the party, we can refer to the pricing structure given for the different ranges of guests:

• $100 for the first 10 people (0 to 10 guests)
• $150 for more than 10 and up to 20 people (10 < guests ≤ 20)
• $200 for more than 20 and up to 30 people (20 < guests ≤ 30)
• $250 for more than 30 and up to 40 people (30 < guests ≤ 40)
• $275 for more than 40 and up to 50 people (40 < guests ≤ 50)

Since Rafael wants to spend exactly $250, we look at the range of guests for which the price is $250. According to the pricing structure, $250 is charged for more than 30 and up to 40 guests. Therefore, the range of guests he can invite is:

30 < x ≤ 40

So the correct response is 30<x≤40.