Question

The relationship between the cost of playing a game and the number of games played is given by the equation $c=\$(3n+2)$, where c is the total cost of playing the game in dollars, n is the number of games played, and $\$2$ is the rent of game equipment.

Which of the following statements correctly calculates the cost of playing 4 games?

• A. Cost of playing 4 games = $14, n is a independent variable
• B. Cost of playing 4 games = $12, c is a dependent variable.
• C. Cost of playing 4 games = $14, c is an independent variable.
• D. Cost of playing 4 games = $8, n is a dependent variable.

Answer 1

The correct option is A Cost of playing 4 games = $14, n is a independent variable

Total cost of playing the game $=\$c$
Number of games played = n
Cost of playing n games $\left(c\right)=\$(3n+2)$
Since the total cost of playing the game depends on the number of games played, the total cost is a dependent variable. So, c is the dependent variable.
Since the number of games played does not depend on the total cost of playing the game, the number of games played is an independent variable. So, n is the independent variable.

The cost of playing 4 games can be calculated by substituting the value of n as 4 in the equation $c=\$(3n+2)$.
Now, $c=\$(3n+2)=\$(3\times 4+2)=\$(12+2)=\$14$
So, the cost of playing 4 games is $\$14$. Hence, option c is the correct statement.