A family is choosing a console that is the best for their family. Look at the options below carefully and use them to help the family choose the best option.

Question

X Cube = $300
X Cube Game Card [Supreme]: $20/month, Access to 200 free games, Online access
X Cube Game Card [Awesome]: $17/month, Access to 150 free games, Online access
X Cube Game Card [Great]: $13/month, Access to 100 free games, No online access
X Cube Game Card [Standard]: $9/month, Access to 50 free games, No online access
New games are approximately $60 each.

Workstation = $500
Workstation Game Card [ Card 3]: $20/month, Access to 200 free games, Online access
Workstation Game Card [Card 2]: $17/month, Access to 100 free games, Online access
Workstation Game Card [Card 1]: $13/month, Access to 50 free games, No online access
New games are approximately $50 each.

Mathtendo = $300
Mathtendo Game Card [Gold]: $20/month, Access to 200 free games, Local wireless play access
Mathtendo Game Card [Silver]: $17/month, Access to 150 free games, No online access
New games are approximately $30 each
No battle royale games are included with this gaming system
If the family has a budget of $750 total for games, what would be their best option and why?

Answer 1

To help the family choose the best gaming console within their budget of $750, we'll analyze the total cost including the initial console cost and the best game card options for each console. We will also consider the value of the free games available and the cost of new games upfront for each console.

1. X Cube

• Console cost: $300
• Best monthly game card option: Supreme ($20/month)
• Number of free games: 200
• Cost of new games: $60 each
• Total cost for the first year with the Supreme card:
  • Yearly Game Card Cost: $20 * 12 = $240
  • Total cost (Console + Yearly Card): $300 + $240 = $540

2. Workstation

• Console cost: $500
• Best monthly game card option: Card 3 ($20/month)
• Number of free games: 200
• Cost of new games: $50 each
• Total cost for the first year with Card 3:
  • Yearly Game Card Cost: $20 * 12 = $240
  • Total cost (Console + Yearly Card): $500 + $240 = $740

3. Mathtendo

• Console cost: $300
• Best monthly game card option: Gold ($20/month)
• Number of free games: 200
• Cost of new games: $30 each
• Total cost for the first year with the Gold card:
  • Yearly Game Card Cost: $20 * 12 = $240
  • Total cost (Console + Yearly Card): $300 + $240 = $540

Comparison

Total Costs:

• X Cube Total: $540
• Workstation Total: $740
• Mathtendo Total: $540

Available Budget: $750

Conclusion

Both the X Cube and Mathtendo cost a total of $540, while the Workstation costs $740. All three options allow access to a substantial number of free games, fitting within the given budget.

Best Recommendation:

• If the family prefers access to a wider selection of free games and doesn't mind the monthly fee, either the X Cube or Mathtendo would be a great choice, particularly because they both allow them to save money compared to the Workstation.

The Mathtendo is particularly appealing due to the lower cost of new games ($30 each) compared to new games for the X Cube and Workstation. Additionally, if the family prioritizes local wireless play (which the Mathtendo offers), the Mathtendo might slightly edge out the other options.

Ultimately, if game costs and features are prioritized, Mathtendo might be the best choice provided they are not specifically looking for battle royale games.

Answer 2

The following question is related to all that you just said about the gaming console: What would the solution of this equation tell you?: 300 + 17x = 750

Answer 3

The equation \(300 + 17x = 750\) represents a situation where a family is considering the total cost of a gaming console and the monthly game card fees to determine how many months they can afford to pay for the game card within a budget of $750.

Here's the breakdown of the equation:

1. 300: This is the initial cost of the gaming console.
2. 17: This is the monthly fee for the Awesome Game Card for the X Cube.
3. \(x\): This represents the number of months the family plans to pay for the game card.
4. 750: This is their total budget.

Solving the Equation

To solve the equation for \(x\):

1. Subtract 300 from both sides: \[ 17x = 750 - 300 \] \[ 17x = 450 \]

2. Divide both sides by 17: \[ x = \frac{450}{17} \approx 26.47 \]

Interpretation

The solution, \(x \approx 26.47\), tells you that if the family were to allocate their entire budget of $750 towards purchasing the X Cube console and paying for the Awesome Game Card at $17 per month, they could afford approximately 26 months of the game card.

Since they can only pay for whole months, this means they could afford 26 months of the awesome game card and have some remaining budget (since \(17 \times 26 = 442\)), leaving them with around $8 left over after spending $300 on the console and $442 on the card.

Conclusion

The equation gives the family an idea of how many months they can access the game card when considering their total budget. If they want to maximize their access to games beyond 26 months or consider other game card options, they would need to adjust their budgeting or look into different consoles or plans.

Answer 4

this question is also related: Create and solve an equation that would determine the total cost for the purchase of only new games with no game cards based on the family's budget of $750

Answer 5

To create an equation that determines the maximum number of new games the family can purchase based on their budget of $750 without involving any game cards, we first need to consider the prices of new games for each console.

Step 1: Define Variables

Let:

• \( g \) = number of new games purchased
• The cost of new games for each console is as follows:
  • X Cube: $60 per game
  • Workstation: $50 per game
  • Mathtendo: $30 per game

Step 2: Create Equations for Each Console

1. For the X Cube: \[ 60g = 750 \]

2. For the Workstation: \[ 50g = 750 \]

3. For the Mathtendo: \[ 30g = 750 \]

Step 3: Solve Each Equation

1. X Cube: \[ g = \frac{750}{60} = 12.5 \] This means the family can purchase up to 12 new games for the X Cube (since they can't purchase half a game, they can afford 12 games).

2. Workstation: \[ g = \frac{750}{50} = 15 \] This means the family can afford to purchase up to 15 new games for the Workstation.

3. Mathtendo: \[ g = \frac{750}{30} = 25 \] This means the family can afford to purchase up to 25 new games for the Mathtendo.

Summary

• X Cube: 12 new games at $60 each
• Workstation: 15 new games at $50 each
• Mathtendo: 25 new games at $30 each

Conclusion

If the family chooses to spend their budget entirely on new games, they can purchase:

• Up to 12 games for the X Cube,
• Up to 15 games for the Workstation,
• Up to 25 games for the Mathtendo.

This analysis demonstrates how many new games they can obtain without purchasing game cards, effectively maximizing their gaming library based on their console choice and budget.