To determine the maximum number of texts you can send each month without exceeding your budget, let's break down the problem step-by-step:
1. Understanding the Costs:
- The base cost of your monthly plan is \[tex]$40.
- Each text message costs \$[/tex]0.03 (which is 3 cents).
2. Setting up the Inequality:
- You have a total budget of \[tex]$130 per month.
- Let \( T \) represent the number of texts you can send in a month.
- The total monthly cost would therefore be the sum of the base plan and the cost of the texts, which is given by:
\[
40 + 0.03T
\]
3. Formulating the Inequality:
- Your total expense should not exceed your budget of \$[/tex]130. So, the inequality can be formulated as:
[tex]\[
40 + 0.03T \leq 130
\][/tex]
4. Solving the Inequality:
- First, isolate the variable term by subtracting 40 from both sides:
[tex]\[
0.03T \leq 130 - 40
\][/tex]
[tex]\[
0.03T \leq 90
\][/tex]
- Next, solve for [tex]\( T \)[/tex] by dividing both sides by 0.03:
[tex]\[
T \leq \frac{90}{0.03}
\][/tex]
[tex]\[
T \leq 3000
\][/tex]
5. Conclusion:
- Since you cannot send a fraction of a text, the maximum number of texts you can send each month, while staying within the budget, is 3000 texts.
Therefore, the inequality that determines the number of texts you can send without exceeding your monthly budget is:
[tex]\[
T \leq 3000
\][/tex]
