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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Farid is going to hire a makeup artist for a fashion show and is comparing prices. Audrey charges as a booking fee and an additional per hour. Stanley charges per hour, plus a booking fee of . Depending on the length of the show, the cost could end up being the same for either artist. How long would the show be? What would the cost be?If the show lasted for _____ hours, the cost would always be _____.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Farid is going to hire a makeup artist for a fashion show and is comparing prices. Audrey charges as a booking fee and an additional per hour. Stanley charges per hour, plus a booking fee of . Depending on the length of the show, the cost could end up being the same for either artist. How long would the show be? What would the cost be?If the show lasted for _____ hours, the cost would always be _____.
- Define Variables: Let's define the variables:Let be the number of hours the show lasts.Let be the total cost for hiring the makeup artist.Now, let's write the equations for each makeup artist based on the given information.For Audrey:Booking fee = Charge per hour = Total cost equation:
- Write Equations: For Stanley:Booking fee = Charge per hour = Total cost equation:
- Set Equations Equal: We want to find out when the cost would be the same for either artist, so we set the two equations equal to each other to solve for .
- Solve for x: Now, we solve for x by subtracting from both sides of the equation:
- Substitute : Next, we subtract from both sides of the equation to solve for :
- Find Total Cost: Now that we have the value of , we can substitute it back into either of the original equations to find the total cost . We'll use Audrey's equation:
