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?

Question

(1 point)
Responses

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

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

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

20<x≤30

Answer 1

To determine how many people Rafael can invite while spending $250, let's analyze the cost structure:

• For 10 or fewer people: $100
• For more than 10 and up to 20 people: $150
• For more than 20 and up to 30 people: $200
• For more than 30 and up to 40 people: $250
• For more than 40 and up to 50 people: $275

Since Rafael wants to spend $250, the only option that matches this budget is to have more than 30 and up to 40 people.

Thus, the correct range for the number of people Rafael can invite is:

30 < x ≤ 40

The final correct response is: 30<x≤40 (30 less than x less-than-or-equal-to 40)