The total 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 that the one-time cost to be able to make cards is $100, 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?
Let's start by figuring out the repeated cost per card:
- To make 500 cards, the repeated cost is $1,100 - $100 = $1,000. So the cost per card is $1,000 / 500 = $2.
- To make 650 cards, the repeated cost is $1,400 - $100 = $1,300. So the cost per card is $1,300 / 650 = $2.
Now we have enough information to estimate the total cost for 1,000 cards:
- To make 1,000 cards, the one-time cost is still $100.
- The repeated cost per card is $2, so the total repeated cost is $2 * 1,000 = $2,000.
- Therefore, the total cost for 1,000 cards is $100 + $2,000 = $2,100.
To solve this problem, we can use the equation for the total cost:
Total Cost = One-time costs + (Repeated costs per card * Number of cards)
Let's denote the repeated costs per card as R.
Given:
One-time costs = $100
Number of cards (n1) = 500, with the corresponding total cost (tc1) = $1,100
Number of cards (n2) = 650, with the corresponding total cost (tc2) = $1,400
Using the above information, we can set up two equations:
tc1 = One-time costs + (n1 * R)
tc2 = One-time costs + (n2 * R)
Substituting the given values, we get:
$1,100 = $100 + (500 * R)
$1,400 = $100 + (650 * R)
Now we can solve these two equations to find the value of R.
By subtracting $100 from both sides of equation 1:
(500 * R) = $1,000
Dividing both sides by 500:
R = $2
Now that we have the value of R, we can find the total cost for 1,000 cards by using the same equation:
Total Cost = One-time costs + (Repeated costs per card * Number of cards)
Number of cards (n3) = 1,000
Total Cost = $100 + (1,000 * $2)
Total Cost = $100 + $2,000
Total Cost = $2,100
Therefore, the total cost to make 1,000 cards is $2,100.