Under her cell phone plan, Mariana pays a flat cost of $47.50 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 Mariana can use while staying within her budget?
Answer
Multiple Choice Answers
3, left parenthesis, 47, point, 5, plus, x, right parenthesis, is less than, 803(47.5+x)<80
3, left parenthesis, 47, point, 5, plus, x, right parenthesis, is greater than, 803(47.5+x)>80
80, is greater than, 47, point, 5, plus, 3, x80>47.5+3x
80, is less than, 47, point, 5, plus, 3, x80<47.5+3x

To determine the correct inequality for the problem:

Mariana pays:
- A flat cost of \$47.50 per month.
- \$3 per gigabyte of data used.

She wants her total bill to stay **under \$80 per month**. We can model her total cost as:
\[
\text{Total Cost} = 47.50 + 3x
\]
where $x$ is the number of gigabytes used.

She wants this total cost to be **less than or equal to** \$80. So, the inequality is:
\[
47.50 + 3x \leq 80
\]
This can be rearranged as:
\[
80 \geq 47.5 + 3x
\]
which matches the third multiple choice option.

Therefore, the correct inequality is:
\[
80 \geq 47.5 + 3x
\]

Would you like details or have any questions? Here are some additional related questions:

1. How can you solve this inequality to find the maximum number of gigabytes?
2. What would happen if Mariana wanted to spend exactly $80?
3. How would the inequality change if the cost per gigabyte increased to $5?
4. How would the inequality change if the flat rate decreased to $40?
5. What if she had a budget of $100 instead of $80?

**Tip:** Always ensure that inequality symbols accurately represent the situation—use "<" or "≤" for constraints like budget limits.

Under her cell phone plan, Mariana pays a flat cost of $47.50 per month and $3 per gigabyte. She wants to keep her bill under $80 per month. Which inequality can be used to determine x, the maximum number of gigabytes Mariana can use while staying within her budget?

Understand how to solve a linear inequality for a budget constraint in a cell phone plan scenario. Learn the steps to determine the maximum number of gigabytes that can be used while staying under $80. Suitable for students in Grades 7-9, focusing on algebra and inequalities.

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