Question

The cost for a biusness to make greeting cards can be divided into one-time cost (e.g., a printing machine) and repeated costs ( e.g., inc and paper ). Suppose the total cost to make 300 cards is $900.00, and the total cost to make 650 cards is $1,600.00. What is the total cost to make 1,000 cards? Round your answer to the nearest dollar.

Answer 1

It would cost $2300 to print 1000 cards.

I set up a system of equations for this problem.  Let x be the one-time cost (such as a printer) and y be the repeated costs (such as ink and paper).  The one-time cost will be the same no matter how many cards you print.  However the repeated costs will change based on how many cards are printed at a time.

The first equation looks like this:
x+300y=900
because the one time cost, added to the repeated costs for 300 cards, was 900.

The second equation looks like this:
x+650y=1600
because the one time cost, added to the repeated costs for 650 cards, was 1600.

Together the system is:
x+300y=900
x+650y=1600

Since the coefficients of x are the same, we can eliminate x by subtracting the bottom equation:
   x+300y=900
-(x+650y=1600)

Which gives us:
-350y=-700

Divide both sides by -350:
-350y/-350 = -700/-350
y = 2

Substitute that into the first equation:
x+300*2 = 900
x+600=900

Subtract 600 from both sides:
x+600-600=900-600
x=300

The one-time cost is $300 and the repeated costs are $2 per card.

This means that for 1000 cards we have
300+2(1000)=300+2000=2300.