Kabir paid an entrance fee of [tex]\$5[/tex] plus an additional [tex]\$0.75[/tex] per game at a local arcade. The next week, he and a friend went to another arcade where Kabir paid [tex]\$1.25[/tex] per game, but there was no entrance fee. How many games will Kabir have to play at each arcade to spend the same amount of money at each arcade?

Which equation represents how to solve for how many games Kabir will have to play?

A. [tex]5 + 0.75x = 1.25x[/tex]
B. [tex]0.75 + 5x = 1.25x[/tex]
C. [tex]5 + 0.75x = -1.25x[/tex]
D. [tex]0.75 - 5x = 125x[/tex]

To solve the problem of determining how many games Kabir will need to play at each arcade to spend the same amount of money, we need to set up equations for each arcade and find the point where the costs are equal. Let's go through the steps:

1. Understand the costs:
- For the first arcade, Kabir pays an entrance fee and a cost per game. This can be written as:
[tex]\[
\text{Total cost at the first arcade} = 5 + 0.75x
\][/tex]
where [tex]$ x $[/tex] is the number of games played.

- For the second arcade, Kabir only pays for each game without any entrance fee:
[tex]\[
\text{Total cost at the second arcade} = 1.25x
\][/tex]

2. Set the equations equal:
- To find the number of games where both total costs are equal:
[tex]\[
5 + 0.75x = 1.25x
\][/tex]

3. Solve for [tex]$ x $[/tex]:
- First, we'll simplify and solve the equation:
[tex]\[
5 + 0.75x = 1.25x
\][/tex]
- Move [tex]$ 0.75x $[/tex] to the right side:
[tex]\[
5 = 1.25x - 0.75x
\][/tex]
- Simplify the right side:
[tex]\[
5 = 0.5x
\][/tex]
- Divide both sides by 0.5 to solve for [tex]$ x $[/tex]:
[tex]\[
x = \frac{5}{0.5}
\][/tex]
[tex]\[
x = 10
\][/tex]

Therefore, Kabir will have to play 10 games at each arcade to spend the same amount of money. The correct equation representing this scenario is:
[tex]\[
5 + 0.75x = 1.25x
\][/tex]