SOLUTION: stephanie is planning her sweet 16 and wants to have live music and food for everyone who attends. her parents found a dj that will charge them $750 and a caterer who will provide

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Question 1014811: stephanie is planning her sweet 16 and wants to have live music and food for everyone who attends. her parents found a dj that will charge them $750 and a caterer who will provide food and drinks for $2.25 per person. if their goal is to keep the average cost per person between $2.75 and $3.25, how many people, p, must attend.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The total cost is 750 + 2.25p, where p is the number of people to attend. (Also it is safe to assume that p is positive.)
The average cost per person is thus %28750%2B2.25p%29%2Fp, or equivalently 750%2Fp+%2B2.25.
Hence, 2.75+%3C+750%2Fp+%2B2.25+%3C+3.25 as per the restriction on average cost.
Then 0.50+%3C+750%2Fp+%3C+1 after transposing the constant term.
2+%3E+p%2F750+%3E+1 after inverting the double inequality. (Remember all terms are positive.)
Thus 1500>p>750 after cross-multiplication.
Therefore they can have anywhere from 751 to 1499 attendees.