Question 7 of 19
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 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.
A. $2,100.00
B. $2,300.00
C. $2,500.00
D. $3,000.00
7 / 19
First, we need to find the cost per card for each of the two scenarios:
For 300 cards: $900.00 / 300 = $3.00 per card
For 650 cards: $1,600.00 / 650 = $2.46 per card
Next, we can use the cost per card for one of the scenarios to find the total cost for 1,000 cards. Let's use the cost per card from the 300 card scenario:
$3.00 per card x 1,000 cards = $3,000.00
Therefore, the total cost to make 1,000 cards is $3,000.00, which corresponds to answer choice D.
Write a rule for the function represented by the table.
x y
0 14
1 29
2 44
3 59
A. y = 15 + 14x
B. y = 14 + 15x
C. y = 12 + 17x
D. y = 17 + 12x
Looking at the table, we can see that as the value of x increases by 1, the value of y increases by 15. This tells us that there is a constant rate of change of 15 between the x and y values. Additionally, we can see that when x is 0, y is 14, which gives us the y-intercept of the function. Therefore, the rule for this function is:
y = 15x + 14
This matches with answer choice A. Therefore, the correct answer is A.
To find the total cost to make 1,000 cards, you need to determine the cost per card and then multiply it by 1,000.
First, calculate the cost per card at both 300 cards and 650 cards. You can do this by finding the difference in total cost and dividing it by the difference in the number of cards.
For 300 cards:
The total cost is $900.00, and the number of cards is 300.
So, the cost per card at 300 cards is $900.00 / 300 = $3.00.
For 650 cards:
The total cost is $1,600.00, and the number of cards is 650.
So, the cost per card at 650 cards is $1,600.00 / 650 = $2.46.
Now that you have the cost per card at both 300 cards ($3.00) and 650 cards ($2.46), you can estimate the cost per card at 1,000 cards.
To estimate the cost per card at 1,000 cards, you can calculate the average of the two costs per card:
($3.00 + $2.46) / 2 = $2.73.
Finally, multiply the cost per card at 1,000 cards ($2.73) by 1,000 to find the total cost to make 1,000 cards:
$2.73 * 1,000 = $2,730.00.
Rounding this answer to the nearest dollar, the total cost to make 1,000 cards is approximately $2,730.00.
Therefore, the correct answer is B. $2,300.00.