Question

Andra was comparing the electricity costs of two different companies. One company charges $49 per month and an additional $0.10 per kilowatt used. The other company offers a $39 monthly fee but charges $0.15 for all kilowatts used beyond the first 100 kilowatts. Sandra used the following system of equations to represent the situation:

Ca = 49 + 0.10x
Cb = 39 + 0.15(x - 100)

Which of the following is a reasonable solution to this system of equations, and what does it represent?

Options:
A) Ca = Cb, representing the two companies have the same total cost.
B) Ca < Cb, indicating that the first company is cheaper for any amount of electricity used.
C) Ca > Cb, suggesting that the second company is cheaper for any amount of electricity used.
D) Ca = 0, meaning that Sandra pays nothing for electricity.
E) Ca = $49, indicating that Sandra pays a fixed monthly fee of $49 for electricity.

Answer 1

The given system of equations represents the electricity costs of two different companies. We can solve the system to find the cost of electricity and determine which company is cheaper.

Step-by-step explanation:

The given system of equations represents the electricity costs of two different companies, where Ca represents the cost of the first company and Cb represents the cost of the second company. The equations are:

Ca = 49 + 0.10x

Cb = 39 + 0.15(x - 100)

To determine a reasonable solution, we need to compare the two costs. Let's solve the system of equations:

Ca = 49 + 0.10x

Cb = 39 + 0.15(x - 100)

By equating Ca and Cb, we can find the point where the two costs are equal:

49 + 0.10x = 39 + 0.15(x - 100)

Next, we can solve for x to find the amount of kilowatts used. Once we have the value of x, we can substitute it back into either equation to find the cost. The reasonable solution will correspond to the option that matches the calculated cost.