Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Miss Williamson is getting married soon. She would like to hire a professional who will come to her house and do hair and makeup for the bridal party on her wedding day. She has narrowed it down to two possible choices. A woman from Lancaster Salon charges an initial fee of $40 and then an additional $17 per hour. Alternatively, a team from Beauty by Erica offers a free consultation and then charges a higher hourly rate of $21.

a. If it takes a certain amount of time to finish everyone's hair and makeup, Miss Williamson will end up paying the same amount either way. How long would that take

Answer 1

It would take 10 hours to finish everyone's hair and makeup.

Step-by-step explanation:

The problem sets up two equations based on the costs incurred by the two options for the bridal party's hair and makeup. The first equation considers the cost from Lancaster Salon, combining the initial fee and the hourly rate for 't' hours. The second equation represents the cost from Beauty by Erica, considering only the hourly rate for 't' hours.

By equating the total costs from both options, an equation is formed to find the time 't' that makes both costs equal. Solving this equation reveals that for Miss Williamson to pay the same amount regardless of the chosen option, it would take 10 hours to complete everyone's hair and makeup. This outcome allows her to make an informed decision based on time and cost equivalence between the two choices.