Question

Terri and Donna both sell crafts at two different craft shows each weekend. Terri is charged a 5% commission on the amount of money she earns and pays $35 for her booth. Donna is charged a 3% commission on the amount of money she earns and pays $55 for her booth. On the last weekend in November, Terri and Donna both earned the same amount of money at their craft shows. They both paid their respective craft shows the same total amount of money for their booths and commission.
Set up a system of equations to model the amount of money Terri and Donna pay each weekend at the craft shows. Let x represent the money earned from sales, let T represent the total amount Terri pays in one weekend, and let D represent the total amount Donna pays in one weekend.
What is the solution to the system of equations found in Part A? Give your answer as an ordered pair.
What does the solution of the system of equations found in Part B represent in the context of this situation? Be sure to explain the meaning of the values in the solution.

Answer 1

Answer:

• (x, T) = (x, D) = (1000, 85)
• each booth pays $85 in fees on rental and sales of $1000

Step-by-step explanation:

A. Given

  T = 0.05x +35 . . . . Terri's cost of operating a craft booth

  D = 0.03x +55 . . . . Donna's cost of operating a craft boot

  T = D

where x is the dollar amount of sales.

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B. Solution

Subtracting the equation for D from that of T, we get ...

  T - D = 0

  (0.05x +35) -(0.03x +55) = 0 = 0.02x -20

  0 = x -1000 . . . . . divide by 0.02

  x = 1000

  T = D = 0.05(1000) +35 = 85

  (x, T) = (x, D) = (1000, 85)

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C. Meaning

According to the given definitions of the variables, each booth pays a total of $85 in fees for sales of $1000.