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.