Question

If the yearbook staff sells 50 yearbooks, the cost per yearbook is $45. If they sell 125 yearbooks, the cost per yearbook is $37.50. Assuming a linear equation fits the situation, find the price per yearbook if the staff sells 150 yearbooks

Answer 1

Is total cost linear, or is average cost linear?

Answer 2

Let fixed cost be F and variable cost be V.
Then, cost function is
C(x) = Vx + F

For 50 books, cost per book is $45. Therefore,
45*50 = V*50 + F

For 125 books, cost per book is $37.50. Therefore,
37.50*125 = V*125 + F

On solving the above two equations we get
V = 32.5 and F = 625

Therefore, cost function is
C(x) = 32.5x + 625
When number of books is 150, cost is
C(150) = 32.5*150 + 625 = $5500
Cost per book is
5500/150 = $36.67

Hope it helps.

Answer 3

So its 36 dollars. :)