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.

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.