Merari goes to the local arcade. She has to pay $3.50 for a game card plus a certain rate per game. she plays a total of 15 games, and the final cost is $14.75. Develop a linear model to describe the scenario. What is the amount per game that Merari has to pay?

Question

1)$0.98
2)$0.75
3)$1.22
4)$11.25

Answer 1

Let \( x \) be the cost per game played. The total cost for Merari includes the cost of the game card plus the cost of playing the games. We can set up the equation based on the given information:

1. The cost of the game card is $3.50.
2. The cost for playing 15 games is \( 15x \).
3. The total cost is $14.75.

The equation representing the total cost is: \[ 3.50 + 15x = 14.75 \]

To solve for \( x \), first, subtract $3.50 from both sides: \[ 15x = 14.75 - 3.50 \] \[ 15x = 11.25 \]

Next, divide both sides by 15: \[ x = \frac{11.25}{15} \] \[ x = 0.75 \]

Thus, the amount per game that Merari has to pay is \($0.75\).

The correct answer is 2) $0.75.