Let's break down the costs based on the number of people invited to the party:
- 1 to 10 people: $100
- 11 to 20 people: $150
- 21 to 30 people: $200
- 31 to 40 people: $275
- 41 to 50 people: $350
Given that Raphael wants to spend $250, let's determine how many people he can invite for that budget:
- For 1 to 10 people, the cost is $100. (Under budget)
- For 11 to 20 people, the cost is $150. (Under budget)
- For 21 to 30 people, the cost is $200. (Under budget)
- For 31 to 40 people, the cost is $275. (Over budget)
- For 41 to 50 people, the cost is $350. (Over budget)
Since Raphael's budget is $250, he can invite:
- Up to 30 people for $200.
- He cannot afford 31 people (which costs $275).
Therefore, Raphael can invite a maximum of 30 people within his budget of $250.