Final answer:
The Home Cleaning Company becomes less expensive than Power Clean when a house has more than 10 windows. This is found by comparing the costs of both companies and solving for the number of windows at which the cost of The Home Cleaning Company is less than Power Clean.
Step-by-step explanation:
To determine how many windows must a house have to make the total cost from The Home Cleaning Company less expensive than Power Clean, we need to set up two equations and find the point where The Home Cleaning Company becomes cheaper.
The Home Cleaning Company charges $300 for power-washing the siding and $15 per window. So, the total cost for The Home Cleaning Company can be represented as:
CostHome Cleaning = 300 + 15w, where w is the number of windows.
Power Clean charges $45 per window, and this price includes power-washing the siding. Therefore, the total cost for Power Clean is:
CostPower Clean = 45w
To find the number of windows that make the Home Cleaning Company less expensive than Power Clean, we need to solve for w when:
300 + 15w < 45w
Subtracting 15w from both sides gives us:
300 < 30w
Dividing both sides by 30 we get:
w > 10
Therefore, the Home Cleaning Company becomes less expensive than Power Clean when there are more than 10 windows in the house.