How many muffins

Question

A specialty muffin company makes muffins for $0.12 per muffin. The starting cost of the company is $300. How many muffins must the company make before the average cost per muffin is $0.25?

Answer 1

Let x = number of muffins

 

  “$0.12 per muffin”, “with starting cost of $300”

         Average cost = (total cost)/(number of muffins)

                               = ($300 + $0.12x) / x

  “ave  is $0.25”    means  $0.25 = ($300+$0.12x) / x

  “before”   means find the crossover point where costs are equal

 

The math:

  25 = (30000 + 12x)/x        [let’s use cents]

  25x = 30000 + 12x            [multiply both sides by x]

  13x = 30000         [subtract 12x from both sides]

    x = 2308     [divide both sides by 13; must be rounded up to a whole muffin]

 

Check:

  At 2307 muffins,

    Ave. cost = ($300 + $0.12(2307)) / 2307

    Ave. cost = $0.250039    (still just a little high)

  At 2308 muffins,

    Ave. cost = ($300 +$0.12(2308))/2308

    Ave. cost =$0.2499827      [now below $0.25]

Answer 2

Ok, so without considering the starting cost of the company, our muffins are costing us 12¢ a pop. Now we want to find out at what point it will cost us 25¢ a pop when we ARE considering the starting costs.

 

The difference between 25¢ and 12¢ is 13¢, so let's find out how many muffins we have to make for the starting costs to be 13¢ per muffin: 300 / 0.13 = 2,308 rounded to the nearest scrumptious specialty muffin.

 

So, 2,308 is the answer!