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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 :

GinnyAnswer
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]

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