Stella needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4 hours and charged her $59 for parts. The total was $359. Which tape diagram could be used to represent the context if xx represents the cost of labor per hour?

1 answer

To create a tape diagram representing the context of Stella's computer repair costs, we need to break down the total charges into parts for labor and parts.

  1. Total Cost: $359
  2. Cost of Parts: $59
  3. Cost of Labor: This will be represented as \(xx\).

From the information given, we can calculate the total cost of labor. Since the cost of parts is $59, we can find the total cost of labor by subtracting the cost of parts from the total cost:

\[ \text{Total Labor Cost} = \text{Total Cost} - \text{Cost of Parts} = 359 - 59 = 300 \]

Stella was charged for labor at a rate of \(xx\) per hour for 4 hours. Therefore, the cost of labor can also be expressed as:

\[ \text{Cost of Labor} = 4 \cdot xx \]

To represent this in a tape diagram, you could have the following:

  • One segment (bar) representing the cost of parts which equals $59.
  • Another segment (bar) representing the total labor cost of $300, which is made up of 4 smaller segments (each representing 1 hour of labor at a rate of \(xx\)).

This means the tape diagram would look like this:

  • Total cost: One long rectangle representing $359.
    • Divide it into two sections:
      • The first section would be a smaller rectangle for parts: $59.
      • The second section would be a longer rectangle for labor, with 4 smaller subdivisions representing the labor cost of \(4xx\) ($300).

To summarize, the tape diagram consists of:

  • A large rectangle labeled $359 (Total Cost)
  • A smaller adjacent rectangle labeled $59 (Cost of Parts)
  • A longer rectangle labeled $300 with 4 equal smaller segments, each labeled \(xx\) representing the cost of labor per hour.

In conclusion, you could summarize the parts of the diagram as:

  • Total Cost = Cost of Parts + Cost of Labor
  • $359 = $59 + 4 \(xx\)

This representation visually breaks down the cost components of the service Stella received.