Question

Mario wants to play games at video -arcade. He is trying to find arcade based on entry fees and hourly rate:

Invader arcade : $2.50 each hour and $2.50 entrance -fee
Pinball arcade : $2 each hour and $4 entrance -fee
Help Mario to find a better arcade to play games.
Please solve with chart or table and equation

Answer 1

If Mario wants to play for 3hrs or less he should go to Invader arcade, but if he wants to play for more than 3 hours he should go to Pinball arcade.

I attached a photo showing the table and work, hope this helps:)

Answer 2

To find the better arcade, compare the cost functions:
`\(C_{\text{Invader}}(h) = 2.50h + 2.50\)` for Invader and
`\(C_{\text{Pinball}}(h) = 2h + 4\)` for Pinball. Choose the arcade with the lower total cost based on desired gameplay hours.

Mario is deciding between two arcades: Invader Arcade with a $2.50 hourly rate and $2.50 entrance fee, and Pinball Arcade with a $2 hourly rate and $4 entrance fee.

To compare, we can use cost functions based on hours played. For Invader Arcade, the cost function is
`\(C_{\text{Invader}}(h) = 2.50h + 2.50\)`, and for Pinball Arcade, it's
`\(C_{\text{Pinball}}(h) = 2h + 4\)`.

By plugging in different hours, Mario can determine which arcade is more cost-effective for his desired gameplay duration. It's essential for him to consider both the hourly rate and entrance fee to make an informed decision based on his budget and preferences.