To determine how many people Raphael can invite if he wants to spend $250 for the party, let's break down the pricing structure:
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$100 for the first 10 people
- If he invites 10 people or fewer, he pays $100.
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$150 for more than 10 and up to 20 people
- If he invites between 11 and 20 people, he pays $150.
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$200 for more than 20 and up to 30 people
- If he invites between 21 and 30 people, he pays $200.
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$250 for more than 30 and up to 40 people
- If he invites between 31 and 40 people, he pays $250.
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$275 for more than 40 and up to 50 people
- If he invites between 41 and 50 people, he pays $275.
Since Raphael wants to spend up to $250, he can invite up to 40 people.
Thus, the maximum number of people he can invite while staying within his budget is 40.