Under her cell phone plan, Violet pays a flat cost of \[tex]$38 per month and \$[/tex]3 per gigabyte. She wants to keep her bill under \$80 per month. Which inequality can be used to determine [tex]\( x \)[/tex], the maximum number of gigabytes Violet can use while staying within her budget?

A. [tex]\( 80 \ \textgreater \ 3x + 38 \)[/tex]
B. [tex]\( 80 \ \textgreater \ 3(38 + x) \)[/tex]
C. [tex]\( 80 \ \textless \ 3x + 38 \)[/tex]
D. [tex]\( 80 \ \textless \ 3(38 + x) \)[/tex]



Answer :

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]