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C.16 Solve linear equations with variables on both sides: word problemsH9GTina and Shane waited in line all day at Get 'Em Games to buy the new PowerPlay3000 gaming system. Shane got his system for $250.50, and he bought 2 controllers to go with it. Tina, a Get 'Em Games Gold Member, got her system for only $200, and she bought 4 controllers at regular price. Tina and Shane each spent the same amount in total.Which equation can you use to find c, the cost of each controller?How much did each controller cost?$

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To find the cost of each controller, we can set up an equation based on the information given about Tina and Shane's total expenses.

Shane's total cost:

  • Cost of gaming system: $250.50
  • Cost of 2 controllers: \(2c\) (where \(c\) is the cost of each controller)

So, Shane's total expenditure can be expressed as: \[ 250.50 + 2c \]

Tina's total cost:

  • Cost of gaming system: $200
  • Cost of 4 controllers: \(4c\) (where \(c\) is the cost of each controller)

So, Tina's total expenditure can be expressed as: \[ 200 + 4c \]

Since Tina and Shane each spent the same amount, we can set their total expenditures equal to each other: \[ 250.50 + 2c = 200 + 4c \]

Now we can solve for \(c\).

  1. Rearranging the equation: \[ 250.50 - 200 = 4c - 2c \] \[ 50.50 = 2c \]

  2. Divide both sides by 2: \[ c = \frac{50.50}{2} = 25.25 \]

Thus, the cost of each controller is $25.25.

Summary:

  • The equation to solve was \(250.50 + 2c = 200 + 4c\).
  • The cost of each controller \(c\) is $25.25.