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.
A. $2,000
B. $2,100
C. $2,250
D. $2,300
writing your data as ordered pairs, I would get:
(500,1100) and (650,1400)
slope or (change in cost)/(change in number) = (1400-1100)/(650-500)
= 300/150
= 2
so if x is the number of cards and y is the total cost
y = 2x + b
plug in (500,1100)
1100 = 2(500) + b
b = 100
y = 2x + 100 or cost = 2(number of cards) + 100
so if number of cards = 1000, cost = ....
To solve this problem, we can use the concept of the cost per unit.
First, let's calculate the cost per unit for making greeting cards. We can do this by subtracting the one-time costs from the total costs and then dividing by the number of cards produced.
For the first scenario (500 cards), the cost per unit is (Total cost - One-time costs) / Number of cards = ($1,100 - One-time costs) / 500 cards.
Similarly, for the second scenario (650 cards), the cost per unit is (Total cost - One-time costs) / Number of cards = ($1,400 - One-time costs) / 650 cards.
Since the number of one-time costs remains the same in both scenarios (regardless of the number of cards produced), we can equate the cost per unit expressions from the two scenarios:
($1,100 - One-time costs) / 500 = ($1,400 - One-time costs) / 650
Now, let's solve this equation to find the value of One-time costs.
500 * ($1,100 - One-time costs) = 650 * ($1,400 - One-time costs)
550,000 - 500 * One-time costs = 910,000 - 650 * One-time costs
650 * One-time costs - 500 * One-time costs = 910,000 - 550,000
150 * One-time costs = 360,000
One-time costs = 360,000 / 150
One-time costs = $2,400
Now that we have found the one-time costs, we can calculate the total cost to make 1,000 cards.
Total cost to make 1,000 cards = One-time costs + Repeated costs
Repeated costs can be calculated by multiplying the cost per unit by the number of cards (1,000 cards in this case).
Cost per unit = ($1,100 - One-time costs) / 500
Repeated costs = Cost per unit * Number of cards = ($1,100 - $2,400) / 500 * 1,000
Repeated costs = ($-1,300) / 500 * 1,000 (Note: We are using the calculated value for One-time costs)
Repeated costs = $-2.60 * 1,000
Repeated costs = -$2,600
Total cost to make 1,000 cards = One-time costs + Repeated costs
Total cost to make 1,000 cards = $2,400 + (-$2,600)
Total cost to make 1,000 cards = $-200
However, since the cost cannot be negative, the total cost to make 1,000 cards should be rounded to zero.
Therefore, the answer is $0.
To determine the total cost to make 1,000 cards, we need to find the relationship between the number of cards and the total cost. In this case, we are given the total cost for two different quantities of cards: 500 cards and 650 cards.
First, let's find the difference in cost between making 500 cards and making 650 cards:
$1,400 - $1,100 = $300
This $300 represents the cost for an additional 150 cards (650 - 500 = 150). Therefore, the cost per additional card is:
$300 / 150 = $2
Now, let's find the total cost for 1,000 cards. We already know the total cost for 650 cards is $1,400. To find the cost for the additional 350 cards (1,000 - 650 = 350), we multiply the cost per additional card ($2) by the number of additional cards:
$2 * 350 = $700
Adding the cost for 650 cards ($1,400) to the cost for the additional 350 cards ($700) gives us the total cost to make 1,000 cards:
$1,400 + $700 = $2,100
Therefore, the total cost to make 1,000 cards is $2,100.
The correct answer is B. $2,100.