Question

The cost for a business to make greeting cards can be divided into one-time costs (e.g., a printing machine) and repeated costs (e.g., ink and paper). Suppose the total cost to make 500 cards is $1,100, and the total cost to make 650 cards is $1,400. What is the total cost to make 1,000 cards? Round your answer to the nearest dollar.

Answer 1

$2100

Explanation:

We can make direct use of the fact that the repeated costs are proportional to the number of cards. That lets us write an equation based on the change in cost.

Setup

The change in cost per card from 500 to 650 cards will be the same as the change in cost per card from 500 to 1000 cards. Using c as the cost to make 1000 cards, we have ...

(1400 -1100)/(650 -500) = (c -1100)/(1000 -500)

Solution

Multiplying by (150)(500), we have ...

500(300) = (150)(c -1100)

1000 = c -1100 . . . . . divide by 150

2100 = c

The total cost to make 1000 cards is $2100.

Additional comment

One of the intermediate equations shows us it costs $1100 to make 500 cards and $1000 to make 500 additional cards. This tells us the one-time costs are $100, and the repeated costs are $2 per card. You notice we did not actually have to find these values in order to solve the problem.