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

Question

Victor is a plumber, and his coworker Pablo is an electrician. Victor charges customers a fee of $111 just to come to their houses and then $1 per minute that he is there. Pablo also charges a fee of $37 for a home visit, plus an additional $3 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?

Victor and Pablo each earned $
by working for
minutes.

Answer 1

Let \( t \) represent the time in minutes that both Victor and Pablo spent working.

The equations for their total earnings can be set up as follows:

1. Victor's earnings: \( V = 111 + 1t \)
2. Pablo's earnings: \( P = 37 + 3t \)

According to the problem, they earned the same amount, so we can set the equations equal to each other:

\[ 111 + 1t = 37 + 3t \]

Now, let's solve the equation for \( t \).

First, we can simplify by moving all terms involving \( t \) to one side and constant terms to the other:

\[ 111 - 37 = 3t - 1t \]

\[ 74 = 2t \]

Now, divide both sides by 2:

\[ t = 37 \]

Now that we know the time spent working, we can find how much each earned.

Calculating Victor's earnings: \[ V = 111 + 1(37) = 111 + 37 = 148 \]

Calculating Pablo's earnings: \[ P = 37 + 3(37) = 37 + 111 = 148 \]

Thus, we find:

Victor and Pablo each earned $148 by working for 37 minutes.

Filling in the blanks:

Victor and Pablo each earned $148 by working for 37 minutes.