Under his cell phone plan, Carlos pays a flat cost of $57 per month and $5 per gigabyte. He wants to keep his bill under $65 per month. Write and solve an inequality which can be used to determinez, the number of gigabytes Carlos can use while staying within his budget.

Question

Inequality:

x ( <, >, ≥, ≤ ) ____

Answer 1

To establish the inequality for Carlos's cell phone plan, we need to consider his flat monthly cost of $57 and the additional cost of $5 per gigabyte used. He wants to keep his total monthly bill under $65.

Let's define \(x\) as the number of gigabytes Carlos uses. The total cost of his plan can be expressed as:

\[ \text{Total Cost} = 57 + 5x \]

Since Carlos wants his bill to be less than $65, we can set up the following inequality:

\[ 57 + 5x < 65 \]

Now, we'll solve the inequality:

1. Subtract 57 from both sides:

\[ 5x < 65 - 57 \]

\[ 5x < 8 \]

2. Divide both sides by 5:

\[ x < \frac{8}{5} \]

\[ x < 1.6 \]

Since \(x\) represents the number of gigabytes, we can only use whole numbers (0, 1, etc.). Therefore, the maximum whole number of gigabytes Carlos can use while staying under $65 is 1 GB.

Inequality: \[ x < 1.6 \] and the practical solution for \(x\) is \(x \leq 1\) (in whole numbers).