Plumber chargers $60 an hour. Plumber B chargers $40 to visit your home plus $55 for each hour. for hop many hours will the total cost for each plumber be the same? how much will that cost be?
Define your variables:
Write a system of equations:
solve the system of equation using either subitution or elimination
I assume the first is plumber A
Cost = 60t , where t is the number of hours
plumber B:
cost = 55t + 40
when are the costs the same? When
60t = 55t+40
solve and you got the value of t
plug it back into one of the equations to get the cost
(no system of equations needed here)
Let's define our variables to solve this problem.
Let x be the number of hours.
For Plumber A, the total cost (C) can be calculated using the equation:
C = 60x
For Plumber B, the total cost (C) can be calculated using the equation:
C = 40 + 55x
Now, we will set up a system of equations using these equations:
Equation 1: C(A) = 60x
Equation 2: C(B) = 40 + 55x
To find out when the total cost for each plumber will be the same, we need to set the two equations equal to each other.
Setting up the equation:
60x = 40 + 55x
Now we can solve this equation using either subtitution or elimination method. Let's use the elimination method.
60x - 55x = 40
5x = 40
x = 40/5
x = 8
So, the total cost for each plumber will be the same after 8 hours of work.
To find out the total cost for both plumbers at that time, we can substitute the value of x into either equation.
Using Equation 1 (C(A) = 60x):
C(A) = 60 * 8
C(A) = 480
The total cost for Plumber A will be $480 after 8 hours.
Using Equation 2 (C(B) = 40 + 55x):
C(B) = 40 + 55 * 8
C(B) = 40 + 440
C(B) = 480
The total cost for Plumber B will also be $480 after 8 hours.
Therefore, the total cost for both plumbers will be $480 after 8 hours of work.
Let's define the variables:
Let 'x' be the number of hours for which the total cost will be the same for both plumbers.
Let 'T' be the total cost.
For Plumber A: T = 60x
For Plumber B: T = 40 + 55x
Now, let's set up the system of equations:
60x = 40 + 55x
Simplifying the equation:
60x - 55x = 40
5x = 40
Dividing both sides by 5:
x = 40/5
x = 8
Therefore, the total cost will be the same for both plumbers when the number of hours is 8.
Calculating the cost for each plumber using this value of 'x':
For Plumber A: T = 60(8) = $480
For Plumber B: T = 40 + 55(8) = $480
So, the total cost for both plumbers will be $480 when the number of hours is 8.