The Yearly Cost In Dollars, \[$ Y \$\], For A Member At A Video Game Arcade Based On The Total Game Tokens Purchased, \[$ X \$\], Is Given By The Equation:$\[ Y = \frac{1}{10} X + 60 \\]A Nonmember Pays \$0.20 Per Game Token

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The Yearly Cost in Dollars for a Member at a Video Game Arcade

Understanding the Equation

The yearly cost in dollars, { y $}$, for a member at a video game arcade based on the total game tokens purchased, { x $}$, is given by the equation: y=110x+60{ y = \frac{1}{10} x + 60 }. This equation represents a linear relationship between the total game tokens purchased and the yearly cost incurred by the member. In this equation, { x $}$ represents the total number of game tokens purchased, and { y $}$ represents the corresponding yearly cost.

Interpreting the Equation

To understand the equation, let's break it down into its components. The term 110x{ \frac{1}{10} x } represents the cost per game token, which is { 0.10 $}$. This means that for every game token purchased, the member incurs a cost of { 0.10 $}$. The term 60{ 60 } represents a fixed cost, which is { 60 $}$. This means that the member incurs a fixed cost of { 60 $}$ regardless of the number of game tokens purchased.

Graphing the Equation

To visualize the relationship between the total game tokens purchased and the yearly cost incurred, we can graph the equation. The graph of the equation is a straight line with a slope of 110{ \frac{1}{10} } and a y-intercept of 60{ 60 }. The x-axis represents the total number of game tokens purchased, and the y-axis represents the corresponding yearly cost.

Nonmember Costs

A nonmember pays { 0.20 $}$ per game token. This means that if a nonmember purchases { x $}$ game tokens, the total cost incurred would be { 0.20x $}$. To compare the costs of members and nonmembers, we can graph the equation y=0.20x{ y = 0.20x } on the same graph as the equation y=110x+60{ y = \frac{1}{10} x + 60 }.

Comparing Member and Nonmember Costs

By comparing the two equations, we can see that the cost per game token for members is { 0.10 $}$, which is half the cost per game token for nonmembers. However, members incur a fixed cost of { 60 $}$, which is not incurred by nonmembers. This means that members will incur a lower cost per game token, but will also incur a fixed cost that is not incurred by nonmembers.

Solving for x

To solve for { x $}$, we can set the two equations equal to each other and solve for { x $}$. This will give us the total number of game tokens that must be purchased in order for the member's cost to be equal to the nonmember's cost.

Solving for y

To solve for { y $}$, we can substitute the value of { x $}$ into one of the equations and solve for { y $}$. This will give us the corresponding yearly cost incurred by the member.

Real-World Applications

The equation y=110x+60{ y = \frac{1}{10} x + 60 } has real-world applications in the video game arcade industry. For example, the arcade may use this equation to determine the optimal number of game tokens to sell in order to maximize revenue. The arcade may also use this equation to determine the optimal price to charge for game tokens in order to maximize profit.

Conclusion

In conclusion, the equation y=110x+60{ y = \frac{1}{10} x + 60 } represents a linear relationship between the total game tokens purchased and the yearly cost incurred by a member at a video game arcade. The equation can be used to determine the optimal number of game tokens to sell and the optimal price to charge for game tokens in order to maximize revenue and profit.

References

  • [1] "Linear Equations" by Math Open Reference
  • [2] "Graphing Linear Equations" by Math Is Fun
  • [3] "Real-World Applications of Linear Equations" by Khan Academy

Additional Resources

  • [1] "Linear Equations" by Wolfram Alpha
  • [2] "Graphing Linear Equations" by GeoGebra
  • [3] "Real-World Applications of Linear Equations" by MIT OpenCourseWare
    The Yearly Cost in Dollars for a Member at a Video Game Arcade: Q&A

Frequently Asked Questions

We have received many questions about the equation y=110x+60{ y = \frac{1}{10} x + 60 } and its applications in the video game arcade industry. Below are some of the most frequently asked questions and their answers.

Q: What is the cost per game token for a member at a video game arcade?

A: The cost per game token for a member at a video game arcade is { 0.10 $}$.

Q: What is the fixed cost for a member at a video game arcade?

A: The fixed cost for a member at a video game arcade is { 60 $}$.

Q: How does the cost per game token for a member compare to the cost per game token for a nonmember?

A: The cost per game token for a member is { 0.10 $}$, which is half the cost per game token for a nonmember, who pays { 0.20 $}$ per game token.

Q: What is the optimal number of game tokens to sell in order to maximize revenue?

A: The optimal number of game tokens to sell in order to maximize revenue can be determined by using the equation y=110x+60{ y = \frac{1}{10} x + 60 } and solving for { x $}$.

Q: How can the equation y=110x+60{ y = \frac{1}{10} x + 60 } be used to determine the optimal price to charge for game tokens?

A: The equation y=110x+60{ y = \frac{1}{10} x + 60 } can be used to determine the optimal price to charge for game tokens by setting the revenue from selling game tokens equal to the cost of producing game tokens and solving for the price.

Q: What are some real-world applications of the equation y=110x+60{ y = \frac{1}{10} x + 60 } in the video game arcade industry?

A: Some real-world applications of the equation y=110x+60{ y = \frac{1}{10} x + 60 } in the video game arcade industry include determining the optimal number of game tokens to sell in order to maximize revenue, determining the optimal price to charge for game tokens, and optimizing the production and distribution of game tokens.

Q: Can the equation y=110x+60{ y = \frac{1}{10} x + 60 } be used to compare the costs of members and nonmembers?

A: Yes, the equation y=110x+60{ y = \frac{1}{10} x + 60 } can be used to compare the costs of members and nonmembers by graphing the equation and comparing the costs of members and nonmembers at different levels of game token purchases.

Q: How can the equation y=110x+60{ y = \frac{1}{10} x + 60 } be used to determine the break-even point for a video game arcade?

A: The equation y=110x+60{ y = \frac{1}{10} x + 60 } can be used to determine the break-even point for a video game arcade by setting the revenue from selling game tokens equal to the cost of producing game tokens and solving for the number of game tokens that must be sold in order to break even.

Conclusion

In conclusion, the equation y=110x+60{ y = \frac{1}{10} x + 60 } is a powerful tool for determining the optimal number of game tokens to sell and the optimal price to charge for game tokens in the video game arcade industry. By using this equation, video game arcades can maximize revenue and profit, and optimize the production and distribution of game tokens.

References

  • [1] "Linear Equations" by Math Open Reference
  • [2] "Graphing Linear Equations" by Math Is Fun
  • [3] "Real-World Applications of Linear Equations" by Khan Academy

Additional Resources

  • [1] "Linear Equations" by Wolfram Alpha
  • [2] "Graphing Linear Equations" by GeoGebra
  • [3] "Real-World Applications of Linear Equations" by MIT OpenCourseWare