Question

Write a system of equations to describe the situation below, solve using substitution, and fill

in the blanks.
Paul is a plumber, and his coworker Neil is an electrician. Paul charges customers a fee of $59
just to come to their houses and then $3 per minute that he is there. Neil also charges a fee
of $77 for a home visit, plus an additional $1 per minute. Last week the coworkers went to a
job site together, spent the same amount of time working, and earned the same amount.
How much did each one earn? How much time did each one spend working?
Paul and Neil each earned $
by working for
minutes.


pls helpppp

Answer 1

To solve this problem, we need to set up a system of equations. Paul and Neil each earned $86 and spent 9 minutes working.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations. Let's define our variables:

Let x be the number of minutes Paul worked.

Let y be the number of minutes Neil worked.

Paul charges customers $59 just to come to their houses and $3 per minute. So his total earnings are given by the equation: 59 + 3x.

Neil charges customers $77 for a home visit and an additional $1 per minute. So his total earnings are given by the equation: 77 + y.

Since they earned the same amount, we can set their earnings equal to each other:

59 + 3x = 77 + y

This is our first equation.

Next, we know that Paul and Neil spent the same amount of time working. So we can set their minutes equal to each other:

x = y

This is our second equation.

Now we have a system of equations:

59 + 3x = 77 + y

x = y

To solve the system using substitution, we can solve the second equation for x and substitute it into the first equation:

x = y

59 + 3(y) = 77 + y

Simplifying the equation gives us:

2y = 18

y = 9

Substituting y = 9 back into the equation x = y gives us:

x = 9

So Paul and Neil each earned $59 + (3 * 9) = $86 and spent 9 minutes working.