Tina 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.

Question

Which equation can you use to find c, the cost of each controller?
How much did each controller cost?
$

Answer 1

To find the cost of each controller, let's denote the cost of each controller as \( c \).

Shane's total spending:

• Cost of gaming system: $250.50
• Cost of 2 controllers: \( 2c \)

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

Tina's total spending:

• Cost of gaming system: $200
• Cost of 4 controllers: \( 4c \)

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

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

Now, let's solve for \( c \).

1. Subtract \( 2c \) from both sides: \[ 250.50 = 200 + 2c \]

2. Subtract \( 200 \) from both sides: \[ 50.50 = 2c \]

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

Therefore, the cost of each controller is $25.25.