Let's break down the problem step by step to find the inequality that determines the maximum number of gigabytes Violet can use while staying within her budget.
1. Identify Given Costs:
- Violet pays a flat cost of [tex]$ \$[/tex] 38[tex]$ per month.
- She also pays $[/tex] \[tex]$ 3$[/tex] per gigabyte of data used.
2. Define Variables:
- Let [tex]$ x$[/tex] be the number of gigabytes of data Violet uses in a month.
3. Total Monthly Cost:
- The total monthly cost is the sum of the flat cost and the variable cost for data usage.
- Therefore, the total cost [tex]$ C$[/tex] can be expressed as:
[tex]\[
C = \text{flat cost} + (\text{cost per gigabyte} \times \text{gigabytes used})
\][/tex]
- Substituting the given values, we have:
[tex]\[
C = 38 + 3x
\][/tex]
4. Budget Constraint:
- Violet wants to keep her total monthly cost below [tex]$ \$[/tex] 80[tex]$.
- Therefore, we need to set up an inequality where the total monthly cost is less than $[/tex] 80[tex]$:
\[
38 + 3x < 80
\]
5. Reformat the Inequality:
- To match the format of the answer choices provided, let's write the inequality as:
\[
80 > 3x + 38
\]
Thus, the correct inequality that can be used to determine $[/tex] x$, the maximum number of gigabytes Violet can use while staying within her budget, is:
[tex]\[
80 > 3x + 38
\][/tex]
Hence, the correct answer is:
[tex]\[
80 > 3x + 38
\][/tex]
