Question
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?
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Answered by
GPT-4o mini
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.
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.
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