Assuming the prices do not? change, how many copies would the man need to make for the monthly cost of both plans to be the? same?

Question

A man just purchased a high-speed copier for his office and wants a service contract on the copier. HeHe is considering two sources for the contract. The A-1 Copier Sales and Service Company charges $19 a month plus 4 cents a copy. Office Copier Depot charges $25 a month but only 3.5 cents a copy.

Answer 1

Compare the two plans -->   total costs = fixed costs + variable costs

    Note:  variable costs depend on the number of copies made

              [that is, (cost per copy)*(number of copies)]

 

Note: all calculations are per month.

 

Let x = the number of copies per month where total costs are equal.

 

                    Total Costs              =       Fixed Costs       +     Variable Costs

A-1CSSC:            A                     =           $19               +          $0.04x

OCD:                   B                     =           $25               +         $0.035x

 

   [note: these equation are in slope-intercept form:  y= mx+b]

 

 

When are the costs the same (that is, A=B)?

       19000 + 40x = 25000 + 35x          [use tenths of cents; I have trouble with decimals]

            40x = 6000 + 35x          [subtract 19000from both sides]

            5x = 6000              [subtract 35x from both sides]

            x = 1200                [divide both sides by 5]

 

A-1CSSC starts out cheaper, but eh "break-even" point is 1200 copies per month.  Above that, OCD is cheaper.

 

Check:

  Is   $19 + $0.04(1200)= $25 + $0.35(1200)  ?

        $19 + $48.00  =   $25 + $42.00   ?

          $67.00   =   $67.00   ?yes