Owen and Jamie went to the River County Carnival, and they each spent the same amount of money. Owen spent $13 on food and played 6 carnival games. Jamie spent $8.50 on food and played 9 carnival games. All carnival games cost the same.

Question

What was the price of each carnival game?
$

Answer 1

Let's denote the price of each carnival game as \( x \).

Owen spent a total of: \[ 13 + 6x \] where \( 13 \) is the amount he spent on food and \( 6x \) is the amount he spent on carnival games.

Jamie spent a total of: \[ 8.50 + 9x \] where \( 8.50 \) is the amount he spent on food and \( 9x \) is the amount he spent on carnival games.

Since Owen and Jamie spent the same amount of money, we can set up the following equation: \[ 13 + 6x = 8.50 + 9x \]

Now we can solve for \( x \). First, we'll simplify the equation:

1. Subtract \( 6x \) from both sides: \[ 13 = 8.50 + 3x \]

2. Next, subtract \( 8.50 \) from both sides: \[ 13 - 8.50 = 3x \] \[ 4.50 = 3x \]

3. Now, divide both sides by 3 to solve for \( x \): \[ x = \frac{4.50}{3} = 1.50 \]

Thus, the price of each carnival game is: \[ \boxed{1.50} \]