Question
Which of the following situation represents a proportional relationship?
Peter pays $5 for each mile he rides.
Carol receives $2 for each file he completes with a sales tax of 5%.
Albert earns $4 for 30 minutes of work plus $2 for his completion of work.
All of the choices
Peter pays $5 for each mile he rides.
Carol receives $2 for each file he completes with a sales tax of 5%.
Albert earns $4 for 30 minutes of work plus $2 for his completion of work.
All of the choices
Answers
Answered by
GPT-4o mini
A proportional relationship is defined as a relationship where the ratio between two quantities remains constant. Let's analyze each situation:
1. **Peter pays $5 for each mile he rides.**
- This is a proportional relationship because the amount he pays increases linearly with the miles he rides. If he rides 1 mile, he pays $5; for 2 miles, he pays $10; and so on, maintaining a constant ratio of \(5:1\).
2. **Carol receives $2 for each file he completes with a sales tax of 5%.**
- This does not represent a proportional relationship because while Carol earns $2 for every file, the sales tax adds a variable cost that changes based on the total amount earned, thus altering the ratio.
3. **Albert earns $4 for 30 minutes of work plus $2 for his completion of work.**
- This is not a proportional relationship because Albert earns a fixed amount for time worked and an additional fixed amount for completion, which does not maintain a constant ratio. The total earned would vary depending on both the time worked and completion, creating a non-linear relationship.
Considering all these assessments, only Peter's situation represents a proportional relationship. Therefore, the answer is not **"All of the choices."**
The correct conclusion is that **only Peter's situation** represents a proportional relationship.
1. **Peter pays $5 for each mile he rides.**
- This is a proportional relationship because the amount he pays increases linearly with the miles he rides. If he rides 1 mile, he pays $5; for 2 miles, he pays $10; and so on, maintaining a constant ratio of \(5:1\).
2. **Carol receives $2 for each file he completes with a sales tax of 5%.**
- This does not represent a proportional relationship because while Carol earns $2 for every file, the sales tax adds a variable cost that changes based on the total amount earned, thus altering the ratio.
3. **Albert earns $4 for 30 minutes of work plus $2 for his completion of work.**
- This is not a proportional relationship because Albert earns a fixed amount for time worked and an additional fixed amount for completion, which does not maintain a constant ratio. The total earned would vary depending on both the time worked and completion, creating a non-linear relationship.
Considering all these assessments, only Peter's situation represents a proportional relationship. Therefore, the answer is not **"All of the choices."**
The correct conclusion is that **only Peter's situation** represents a proportional relationship.