Two companies charge these rates for printing a brochure :
Company A charges $175 for set up and 0.10 pet brochure
Company B charges $250 for set up and 0.07 pee brochure
A linear system that model this situation is
C=175 + 0.10n
C =250+ 0.07
Where c is the total
A) graph the linear system above (just tellme where x and y intercept is)
B) use the graph to solve these problem
1) how many brosjure must be printed for the cost to be the same at both companies
2) when is it cheaper to use company A to print brocchure ? Explain
ik you cant graph here, but plz can you tell me the x and y intercept so i can do the grpgh
A) To graph the linear system, we need to identify the variables and create the equations. Let's assume that "n" represents the number of brochures printed in both cases:
For Company A: C = 175 + 0.10n
For Company B: C = 250 + 0.07n
Now let's plot the graph:
For Company A:
- The y-intercept is the value of C when n = 0. So, (0, 175) is the y-intercept.
- The x-intercept is the value of n when C = 0. To find the x-intercept, we set C = 0 and solve for n: 0 = 175 + 0.10n. Solving this equation gives you the x-intercept, which is (-1750, 0).
For Company B:
- The y-intercept is the value of C when n = 0. So, (0, 250) is the y-intercept.
- The x-intercept is the value of n when C = 0. To find the x-intercept, we set C = 0 and solve for n: 0 = 250 + 0.07n. Solving this equation gives you the x-intercept, which is (-3571.43, 0).
B) Now, let's use the graph to solve the problems:
1) To find the number of brochures where the costs are the same, we need to find the point where the two lines intersect on the graph. This point represents the number of brochures for which both companies have the same cost. In this case, it is approximately (1080, 283).
2) To determine when it is cheaper to use Company A, we need to compare the y-values (costs) for a given number of brochures. At smaller values of n, Company B's cost is higher. However, at larger values of n, Company A's cost becomes higher due to the difference in the rates. Therefore, it is cheaper to use Company A when the number of brochures is greater than approximately 280 (where the two lines intersect), because Company A's cost starts to increase slower than Company B's cost.
A) To graph the linear system, we need to plot the equations:
Equation 1: C = 175 + 0.10n
Equation 2: C = 250 + 0.07n
The variables in this case are C (total cost) and n (number of brochures).
For the x-intercept, we set C equal to zero in both equations and solve for n:
Equation 1: 0 = 175 + 0.10n --> 0.10n = -175 --> n = -175/0.10 --> n = -1750
Equation 2: 0 = 250 + 0.07n --> 0.07n = -250 --> n = -250/0.07 --> n ≈ -3571.43
Since we cannot have a negative number of brochures, we can round up to the nearest whole number for the x-intercepts:
x-intercept of Equation 1: n = -1750 --> x = -1750
x-intercept of Equation 2: n ≈ -3571.43 --> x ≈ -3571
For the y-intercept, we set n equal to zero in both equations and solve for C:
Equation 1: C = 175 + 0.10(0) --> C = 175
Equation 2: C = 250 + 0.07(0) --> C = 250
The y-intercepts are:
y-intercept of Equation 1: C = 175
y-intercept of Equation 2: C = 250
Therefore, the coordinates of the x and y intercepts are:
x-intercept of Equation 1: (1750, 0)
x-intercept of Equation 2: (-3571, 0)
y-intercept of Equation 1: (0, 175)
y-intercept of Equation 2: (0, 250)
B) Now we can use the graph to solve the problems:
1) To find the number of brochures where the cost is the same for both companies, we need to find the point of intersection on the graph. This point represents the solution to the system of equations. The point of intersection is approximately (-116.67, 137.50). Therefore, around 138 brochures must be printed for the cost to be the same at both companies.
2) To determine when it is cheaper to use company A to print brochures, we compare the costs at different points on the graph. If the y-coordinate of a point on the graph corresponding to company A's equation is lower than the y-coordinate of the corresponding point on the graph for company B's equation, then it is cheaper to use company A. In this case, it is cheaper to use company A when the number of brochures printed is less than approximately 1633.33. Beyond that point, company B becomes cheaper.
Cannot graph here.
1) 175 + 10n = 250 + 7n
Solve for n.
2) numbers < n above