Blake Gives Piano Lessons In The Evenings. He Earns $20 For Each Piano Lesson And Has Between 0 And 6 Lessons Each Evening. The Amount He Earns In An Evening Depends On The Number Of Lessons He Gives. What Is The Range Of This Relation?
Introduction
In this discussion, we will explore the relationship between the number of piano lessons given by Blake in an evening and the amount he earns. We will analyze the given information and determine the range of this relation.
Given Information
- Blake gives piano lessons in the evenings.
- He earns $20 for each piano lesson.
- He has between 0 and 6 lessons each evening.
Understanding the Relationship
Let's denote the number of piano lessons given by Blake in an evening as 'x' and the amount he earns as 'y'. We know that Blake earns $20 for each piano lesson, so the amount he earns is directly proportional to the number of lessons he gives. This can be represented by the equation:
y = 20x
Range of the Relation
To find the range of this relation, we need to determine the possible values of 'y' for the given values of 'x'. Since Blake has between 0 and 6 lessons each evening, the possible values of 'x' are:
0, 1, 2, 3, 4, 5, 6
We can substitute these values into the equation y = 20x to find the corresponding values of 'y':
- For x = 0, y = 20(0) = 0
- For x = 1, y = 20(1) = 20
- For x = 2, y = 20(2) = 40
- For x = 3, y = 20(3) = 60
- For x = 4, y = 20(4) = 80
- For x = 5, y = 20(5) = 100
- For x = 6, y = 20(6) = 120
Conclusion
The range of this relation is the set of all possible values of 'y' for the given values of 'x'. In this case, the range is:
{0, 20, 40, 60, 80, 100, 120}
This means that the amount Blake earns in an evening can be any value between $0 and $120, depending on the number of piano lessons he gives.
Graphical Representation
The relation between the number of piano lessons and the amount earned can be represented graphically as a straight line with a slope of 20. The x-axis represents the number of lessons, and the y-axis represents the amount earned.
Mathematical Representation
The relation can be represented mathematically as a linear equation:
y = 20x
This equation represents the direct proportionality between the number of piano lessons and the amount earned.
Real-World Applications
This type of relation is commonly found in real-world scenarios, such as:
- Sales commissions: A salesperson earns a commission for each sale made, and the amount earned is directly proportional to the number of sales.
- Production costs: A manufacturer earns a profit for each unit produced, and the amount earned is directly proportional to the number of units produced.
Conclusion
Introduction
In our previous discussion, we explored the relationship between the number of piano lessons given by Blake in an evening and the amount he earns. We determined that the range of this relation is {0, 20, 40, 60, 80, 100, 120}. In this article, we will answer some frequently asked questions about Blake's piano lessons.
Q&A
Q: How much does Blake earn for each piano lesson?
A: Blake earns $20 for each piano lesson.
Q: How many piano lessons can Blake give in an evening?
A: Blake can give between 0 and 6 piano lessons in an evening.
Q: What is the range of the relation between the number of piano lessons and the amount earned?
A: The range of the relation is {0, 20, 40, 60, 80, 100, 120}.
Q: Can Blake earn more than $120 in an evening?
A: No, according to the given information, Blake cannot earn more than $120 in an evening.
Q: Can Blake earn less than $0 in an evening?
A: Yes, according to the given information, Blake can earn $0 in an evening if he gives no piano lessons.
Q: Is the relation between the number of piano lessons and the amount earned a linear relation?
A: Yes, the relation is a linear relation, as it can be represented by the equation y = 20x.
Q: Can the relation between the number of piano lessons and the amount earned be represented graphically?
A: Yes, the relation can be represented graphically as a straight line with a slope of 20.
Q: What are some real-world applications of this type of relation?
A: This type of relation is commonly found in real-world scenarios, such as sales commissions, production costs, and more.
Q: Can the relation between the number of piano lessons and the amount earned be represented mathematically?
A: Yes, the relation can be represented mathematically as a linear equation: y = 20x.
Conclusion
In conclusion, we have answered some frequently asked questions about Blake's piano lessons. We hope this Q&A guide has provided you with a better understanding of the relation between the number of piano lessons and the amount earned.
Additional Resources
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Final Thoughts
We hope this Q&A guide has provided you with a better understanding of the relation between the number of piano lessons and the amount earned. If you have any further questions or need additional clarification, please don't hesitate to ask.