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?(1 point)

Question

Responses

$0.75
$0.75

$1.22
$1.22

$11.25
$11.25

$0.98

Answer 1

To develop a linear model for this scenario, we can define the following variables:

• Let \( C \) be the total cost.
• Let \( g \) be the cost per game.
• The fixed cost for the game card is $3.50.
• Merari plays 15 games.

The relationship can be expressed with the following equation:

\[ C = 3.50 + 15g \]

We know that Merari's total cost, \( C \), is $14.75. Thus, we can set up the equation:

\[ 14.75 = 3.50 + 15g \]

Next, we solve for \( g \):

1. Subtract 3.50 from both sides:

\[ 14.75 - 3.50 = 15g \]

\[ 11.25 = 15g \]

2. Divide both sides by 15 to find \( g \):

\[ g = \frac{11.25}{15} \]

\[ g = 0.75 \]

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