Question

Help me plsssssssszzzzzzzzzzzzzzzzz

Answer 1

Answer:

  750 < p < 1500

Step-by-step explanation:

The total cost of the affair for p attendees is ...

  750 +2.25p

The average cost is that number divided by p. The answer choices suggest that "between" means that the cost per person cannot be 2.75 or 3.25. Applying the limits to the average cost, we get ...

  2.75 < (750 +2.25p)/p < 3.25

  2.75 < 750/p + 2.25 < 3.25 . . . . . . . . separating the fraction parts

  0.50 < 750/p < 1.00 . . . . . . . . . . . . . . subtract 2.25

  2 > p/750 > 1 . . . . . . . . . . . . . . . . . . . . . take the reciprocal*

  1500 > p > 750 . . . . . . . . matches choice 4

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* Taking the reciprocals of numbers with the same sign reverses their order:

  2 < 3   but   1/2 > 1/3

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An alternate approach to the solution would be to multiply by p:

  0.50p < 750 < 1.00p

To solve this requires it be made into two inequalities:

  0.50p < 750   ⇒   p < 1500

and

  750 < 1.00p   ⇒   750 < p

Then these would need to be recombined to form the answer:

  750 < p < 1500