Final answer:
To find the total cost at which two different cleaning companies would charge the same amount, we create a system of linear equations based on their respective rates and supply fees, solve for the number of hours where their total costs equal each other, and then calculate the total cost which is $165 for 3 hours of service.
Step-by-step explanation:
The student is asking a question that involves creating and solving a system of linear equations to find out when two cleaning companies charge the same amount for their services. Company 1 charges a flat supply fee of $60 plus $35 per hour. We can represent this with the equation y = 35x + 60, where 'y' is the total cost and 'x' is the number of hours of cleaning provided. Company 2, on the other hand, charges no supply fee but has a rate of $55 per hour, which can be represented by the equation y = 55x.
To find out when both companies charge the same amount (when both equations have the same 'y' value), we set the two equations equal to each other:
35x + 60 = 55x
Subtracting 35x from both sides, we get:
60 = 20x
Dividing both sides by 20, we find:
x = 3
To find the total cost when the charges are the same, we can substitute 'x' back into either of the original equations. Let's use Company 1's equation:
y = 35(3) + 60
= 105 + 60
= $165.
So, the total cost at which both companies would charge the same amount is $165, for 3 hours of cleaning service.