Question

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

Answer 1

38 + 3x < 80

Explanation:

To determine the maximum number of gigabytes (x) Violet can use while staying within her budget, we can set up an inequality.

Violet's monthly cost is the flat fee of $38 plus $3 per gigabyte.

• The flat fee of $38 is a fixed cost that Violet pays every month, regardless of how much data she uses on her cell phone.
• The variable cost, $3 per gigabyte (x), depends on how much data Violet uses during the month. It increases as she uses more gigabytes.

Given that x represents the number of gigabytes used per month, the total monthly cost is given by:

`38 + 3x`

As Violet wants to keep her bill under $80 per month, we set the total cost to less than 80:

`38 + 3x < 80`

So, the inequality that can be used to determine x, the maximum number of gigabytes Violet can use while staying within her budget, is:

`38 + 3x < 80`

To solve for x, begin by subtracting 38 from both sides of the inequality:

`\begin{aligned}38-38+3x& < 80-38\\\\3x& < 42\end{aligned}`

Now, divide both sides by 3:

`\begin{aligned}(3x)/(3)& < (42)/(3)\\\\x& < 14\end{aligned}`

This means Violet must use less than 14 gigabytes to stay within her budget.

Answer 2

38 + 3x < 80

Explanation:

In order t write an inequality to determine the maximum number of gigabytes Violet can use while staying within her budget, we can use the following steps:

Let x be the number of gigabytes Violet uses.

The total cost of her bill will be the flat cost plus the cost of the gigabytes she uses, which is 3x.

3. We want her bill to be under $80, so we can write the following inequality:

Flat cost + Cost of gigabytes < Budget

38 + 3x < 80

This inequality can be used to determine the maximum number of gigabytes Violet can use while staying within her budget.

To solve the inequality, we can subtract 38 from both sides:

3x < 80 - 38

3x < 42

Then, we can divide both sides by 3 to find the maximum number of gigabytes Violet can use:

x < 14

Therefore, the inequality x < 14 can be used to determine the maximum number of gigabytes Violet can use while staying within her budget.