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.
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.
