The cost for a business to make greeting cards can be divided into one-time cost (e.g., a printing machine) and repeated costs (e.g., ink and paper). Suppose the total cost to make 300 cards is $800, and the total cost to make 550 cards is $1,300. What is the total cost to make 1,000 cards? Round your answer to the nearest dollar.
A. $2,000
B. $2,200
C. $2,364
D. $2,667
So, would m = 2, and b = 200? Therefore, the answer would be B, $2,200?
let
b = one-time cost
m = repeated cost per card
Now you know that to print x cards,
300m+b = 800
550m+b = 1300
so, solve for m and b, and then you want 1000m+b
To find the total cost to make 1,000 cards, we can use the concept of proportion. Let's set up a proportion using the given information:
300 cards cost $800
550 cards cost $1,300
We can set up the proportion as:
300 cards / $800 = 550 cards / $1,300
To get the cost of making 1,000 cards, we can multiply both sides of the equation by (1,000/550) since we want to find the cost for 1,000 cards.
(300 cards / $800) * (1,000/550) = (550 cards / $1,300) * (1,000/550)
Simplifying this, we get:
(300 * 1,000) / 550 = (550 * 1,000) / 550
Which further simplifies to:
300,000 / 550 = 1,000
Now, we can find the total cost by dividing 300,000 by 550:
300,000 / 550 = $545.45
Since we need to round the answer to the nearest dollar, the total cost to make 1,000 cards would be $545.
So, the correct answer is not among the options provided.