Under his cell phone plan, Miguel pays a flat cost of $60.50 per month and $3 per gigabyte. He wants to keep his bill at $70.40 per month. Which tape diagram could be used to represent the context if xx represents the number of gigabytes of data Miguel can use while staying within his budget?

Answer 1

To create a tape diagram that represents the context of Miguel's cell phone plan, we start by analyzing his costs.

1. Fixed Cost: Miguel has a flat cost of $60.50 per month.
2. Variable Cost: Miguel pays $3 per gigabyte of data used.
3. Total Budget: Miguel wants to keep his total bill at $70.40 per month.

Now we can set up an equation based on Miguel's costs: \[ \text{Total Cost} = \text{Fixed Cost} + \text{Variable Cost} \] \[ 70.40 = 60.50 + 3x \] where \( x \) represents the number of gigabytes of data.

Next, we want to represent this with a tape diagram.

Tape Diagram Breakdown:

• The first section of the tape could represent the fixed cost ($60.50), which is constant regardless of the number of gigabytes used.
• The remaining portion of the tape must represent the variable cost, which is the additional cost for the number of gigabytes of data Miguel wants to use.
• Since each gigabyte costs $3, the variable section would stretch according to the number of gigabytes.

Construction of the Tape Diagram:

1. Total Tape Length: Label this total length representing $70.40.
2. Fixed Cost Section: A fixed length labeled $60.50, showing the flat rate.
3. Variable Cost Section: The remaining length should be labeled as $3 per gigabyte. This section can be divided into smaller segments, with each segment representing 1 gigabyte of data (like $3 each for \( x \) gigabytes).

Final Setup of the Tape Diagram:

• Start the tape by marking a segment for the fixed cost ($60.50).
• Add a series of smaller segments next to it representing the gigabytes of data, each segment equal to $3.
• The total length of the tape represents Miguel's total budget of $70.40.

This tape diagram visually shows how the fixed and variable costs combine to reach the total amount Miguel can spend, allowing you to easily see how many gigabytes he can afford while staying within his budget.

In summary, the tape diagram will have:

• One solid section for the $60.50 (fixed cost).
• Several segments next to it (each representing $3) until the total reaches $70.40.

To find out how many gigabytes (\( x \)) he can use within his budget, you would solve the equation established.