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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Wanda is looking for a job cutting hair. One option is self-employment at The Lexington Salon, where she would pay per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How much would Wanda pay? How many haircuts would that be?Wanda would pay _____ to either salon if she performed _____ haircuts.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Wanda is looking for a job cutting hair. One option is self-employment at The Lexington Salon, where she would pay per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How much would Wanda pay? How many haircuts would that be?Wanda would pay _____ to either salon if she performed _____ haircuts.
- Set up equations: Set up the system of equations to represent the two options.For The Lexington Salon, Wanda pays a flat rate of per month, regardless of the number of haircuts. This can be represented as:For the franchise, Wanda pays per haircut. If we let 'h' represent the number of haircuts, then the cost can be represented as:We are told that at a certain number of haircuts, the cost to Wanda will be the same for both options. Therefore, we can set the two costs equal to each other to find the number of haircuts 'h' that makes this true:
- Solve for number of haircuts: Solve the equation for '' to find the number of haircuts.To solve for '', we divide both sides of the equation by :
- Calculate franchise cost: Determine how much Wanda would pay if she performed haircuts at the franchise.
- Verify cost for Lexington: Verify that the cost is the same for The Lexington Salon.Since the cost for The Lexington Salon is a flat rate, it remains , which matches the cost calculated for the franchise when Wanda performs haircuts.
