The cost C,of printing a newspaper is partly constant and partly varies as n,the number of printed newspapers.
(1) Express C in terms of n and constants k and h
(2) if the cost of printing 500 newspapers is 320 and of 1000 newspapers is 540,Find the cost of printing 750 newspapers
(1) C = k + hn
(2) We can use the given information to solve for k and h:
320 = k + 500h
540 = k + 1000h
Subtracting the first equation from the second, we get:
220 = 500h
h = 0.44
Substituting this value of h into either equation, we can solve for k:
320 = k + 500(0.44)
320 = k + 220
k = 100
Now we can use the formula from part (1) to find the cost of printing 750 newspapers:
C = 100 + 0.44(750)
C = 430
(1) Let's break down the cost C into its constant and variable parts.
Let's assume the constant cost is represented by k, and the variable cost is represented by h multiplied by the number of printed newspapers (n).
So, the total cost C can be expressed as:
C = k + hn
(2) To find the value of k and h, we can use the given information.
We are told that the cost of printing 500 newspapers is 320, so we can substitute n = 500 and C = 320 into the expression for C:
320 = k + h * 500
Similarly, we are told that the cost of printing 1000 newspapers is 540:
540 = k + h * 1000
Now, we have a system of two equations with two unknowns (k and h). We can solve this system of equations to find their values.
From equation (1): k + h * 500 = 320
From equation (2): k + h * 1000 = 540
Subtracting equation (1) from equation (2), we eliminate k:
h * 1000 - h * 500 = 540 - 320
h * 500 = 220
Dividing both sides by 500:
h = 220/500
h = 0.44
Now we can substitute this value of h back into equation (1) to find the value of k:
k + 0.44 * 500 = 320
k + 220 = 320
k = 320 - 220
k = 100
So, we have k = 100 and h = 0.44.
Now, we can substitute these values back into the expression for C to find the cost of printing 750 newspapers:
C = 100 + (0.44 * 750)
C = 100 + 330
C = 430
Therefore, the cost of printing 750 newspapers is 430.
To express the cost C in terms of n, k, and h, we need to understand how it depends on the number of printed newspapers.
(1) Let's assume that the constant part of the cost is represented by k, and the varying part is represented by h * n. The equation for C can be written as:
C = k + h * n
This means that the total cost C is equal to the sum of the constant cost k and the varying cost h multiplied by the number of newspapers printed n.
(2) Now, let's use the information given to find the value of k and h in order to calculate the cost of printing 750 newspapers.
We are given the following information:
For 500 newspapers: C = 320
For 1000 newspapers: C = 540
Using the equation C = k + h * n, we can substitute the given values:
320 = k + h * 500 (equation 1)
540 = k + h * 1000 (equation 2)
To solve this system of equations, we need to eliminate k. We can do this by subtracting equation 1 from equation 2:
540 - 320 = k + h * 1000 - (k + h * 500)
220 = h * 1000 - h * 500
220 = h * (1000 - 500)
220 = h * 500
Now we can solve for h:
h = 220 / 500
h = 0.44
Substituting the value of h back into equation 1, we can solve for k:
320 = k + 0.44 * 500
320 = k + 220
k = 320 - 220
k = 100
Now that we have the values of k and h, we can calculate the cost of printing 750 newspapers using the equation C = k + h * n:
C = 100 + 0.44 * 750
C = 100 + 330
C = 430
Therefore, the cost of printing 750 newspapers is $430.