Question

HOW DO I SOLVE THIS?

Answer 1

9514 1404 393

Answer:

  (4)  750 < p < 1500

Step-by-step explanation:

The total cost for p people is ...

  c = 750 +2.25p

The average cost per person is this total divided by the number of people:

  c/p = (750 +2.25p)/p

  c/p = (750/p) +2.25

Natasha wants this to be between 2.75 and 3.25:

  2.75 < c/2 < 3.25

  2.75 < 750/p +2.25 < 3.25 . . . . . . use the expression for c/p

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

We can split this to two inequalities to find the limits of p.

Left one

  0.50 < 750/p

  0.50p < 750 . . .multiply by p

  p < 1500 . . . . . . multiply by 2

Right one

  750/p < 1

  750 < p . . . . . . multiply by p

These bounds on p can be summarized as ...

  750 < p < 1500 . . . . matches choice (4)

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Additional comment

Once you realize that the fixed costs will be divided by the number of people attending, the maximum cost you want ($1 more than the per-person charge) will set the minimum number of people. To have the $750 fixed cost contribute only $1 to the cost per person, there must be at least 750 people to share that cost. The only answer choice with a 750 person minimum is (4).