Question

The family arcade center charges an entry fee of $11 plus an additional $1 per game played.Which of the following functions describes the average expense for a player per game played, in terms of x, the number of games played?

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the important parameters

`\begin{gathered} Constant=11\text{ dollars} \\ let\text{ x be the number of games} \\ Variable=1\text{ dollar}* x-numbers\text{ of games played} \\ \therefore Variable=\text{ \$}1x\text{ } \end{gathered}`

STEP 2: Get the total charges for the family arcade center

`\begin{gathered} Total\text{ cost}=Constant+Variable \\ \text{Total Cost}=\text{ \$}11+\text{ \$}1x \end{gathered}`

STEP 3: Write the formula for calculating average expense for playing x numbers of games

`Average=\frac{Cost\text{ of playing games}}{number\text{ of games played}}`
`\begin{gathered} Cost\text{ of playing x-games}=\text{ \$}11+\text{ \$}1x \\ \text{number of games played}=x \end{gathered}`

By substitution,

Hence, the average expense for a player per game played, in terms of x is given by:

`C(x)=\frac{\text{ \$}11+\text{ \$}1x}{x}`

OPTION C