Lauren can spend no more than \$10 at a video game arcade. Each game in the arcade costs [tex]\$0.25[/tex] to play. The inequality [tex]0.25g \leq 10[/tex] can be used to determine the number of games, [tex]g[/tex], she can play with the money she has.

Which number line represents the solution to [tex]0.25g \leq 10[/tex]?

To solve the inequality [tex]$0.25g \leq 10$[/tex] and determine the number of games Lauren can play, let's go through the steps:

1. Understand the inequality: Lauren can spend no more than [tex]$10, and each game costs $[/tex]0.25. We need to find the largest whole number of games she can play without exceeding her budget.

2. Set up the inequality: The inequality given is [tex]$0.25g \leq 10$[/tex], where [tex]$g$[/tex] represents the number of games.

3. Solve for [tex]$g$[/tex]:
- To isolate [tex]$g$[/tex], divide both sides of the inequality by 0.25:
[tex]\[
g \leq \frac{10}{0.25}
\][/tex]
- Perform the division:
[tex]\[
g \leq 40
\][/tex]

4. Interpret the solution: The inequality [tex]$g \leq 40$[/tex] tells us that Lauren can play up to 40 games without spending more than [tex]$10.

5. Number line representation: On a number line, you would represent this solution by a solid dot at 40, shading all numbers to the left of 40, indicating values from 0 to 40 inclusive. This means Lauren can play any number of games from 0 to 40.

Thus, Lauren can play a maximum of 40 games with her $[/tex]10 budget.