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Answer :
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.
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.
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