SOLUTION: A local donut shop has about $10,000 in fixed costs per month. It also costs them about $0.15 in ingredients to produce each donut. In order to make sure they turn a profit each m

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Question 1171613: A local donut shop has about $10,000 in fixed costs per month. It also costs them about $0.15 in
ingredients to produce each donut. In order to make sure they turn a profit each month, they need to
sell enough donuts to bring the average cost per donut down to $3.00 each. About how many donuts do
they need to sell each month bring the average cost down to $3.00 per donut (round decimal answers up
to the next whole number).
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = number of donuts made

1 donut costs $0.15 to make
making x of them cost 0.15x dollars
This is the variable cost.

Add this on top of the $10,000 fixed cost and we have 0.15x+10000 representing the total cost.

Divide this over x to get the average cost
(0.15x+10000)/x

we want this average cost to be $3.00
So we set that x expression equal to 3 and solve for x

(0.15x+10000)/x = 3

0.15x+10000 = 3x

10000 = 3x-0.15x

10000 = 2.85x

2.85x = 10000

x = 10000/2.85

x = 3508.77 approximately

It's not possible to make 0.77 of a donut so we round up to get x = 3509

----------------------------------

Answer: 3509 donuts

Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.

Let n be the number of donuts required.


The wording description, translated to Math, leads to this equation


     = 3.00    (average cost).


From this equation


    10000 + 0.15n = 3n,  or

    10000 = 3n - 0.15n

    10000 = (3-0.15)n

    10000 = 2.85n

      n   = 10000/2.85 = 3508.77 = 3509 (rounded to closest greater integer).    ANSWER

Solved.



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