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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Pedro is a plumber, and his coworker Farid is an electrician. Pedro charges customers a fee of just to come to their houses and then per minute that he is there. Farid also charges a fee of for a home visit, plus an additional 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?Pedro and Farid each earned _____ by working for _____ minutes.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Pedro is a plumber, and his coworker Farid is an electrician. Pedro charges customers a fee of just to come to their houses and then per minute that he is there. Farid also charges a fee of for a home visit, plus an additional 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?Pedro and Farid each earned _____ by working for _____ minutes.
- Define Variables: Let's define the variables.Let be the number of minutes Pedro and Farid worked.Let be the total amount Pedro earned.Let be the total amount Farid earned.Since they both earned the same amount and worked for the same time, we can write the following equations:
- Set Up Equation: Set up the equation that represents they earned the same amount.Since Pedro and Farid earned the same amount, we can set their earnings equal to each other:
- Solve for x: Solve for x.Subtract from both sides:Now subtract from both sides:
- Calculate Total Earned: Calculate the total amount earned by each.Now that we know , we can substitute this value back into the equations for and to find out how much each person earned.For Pedro:For Farid:
- Verify Solution: Verify the solution.We can check our solution by substituting the values of and back into the original equations to ensure they are equal.For Pedro:For Farid:Both equations are true, so our solution is correct.
