Renata Wins A $\$20$ Gift Card To An Online Music Site. After Purchasing 16 Songs, The Gift Card Has A Remaining Balance Of $\$0$[/tex\]. Which Equation Represents The Relationship Between $y$, The Remaining Balance
Understanding the Relationship Between Gift Card Balance and Purchases
Introduction
Renata wins a $20 gift card to an online music site, which she uses to purchase 16 songs. After making these purchases, the gift card has a remaining balance of $0. This scenario presents an opportunity to explore the relationship between the remaining balance on the gift card and the number of songs purchased. In this article, we will delve into the mathematical representation of this relationship and derive an equation that accurately describes it.
The Relationship Between Remaining Balance and Purchases
When Renata purchases songs using her gift card, the remaining balance decreases by the cost of each song. If we denote the remaining balance as y and the number of songs purchased as x, we can establish a relationship between these two variables. The cost of each song is a constant, denoted as c. Therefore, the relationship between y and x can be represented as:
y = 20 - cx
Deriving the Equation
To derive the equation that represents the relationship between y and x, we need to consider the initial balance of the gift card, which is $20. As Renata purchases songs, the remaining balance decreases by the cost of each song. The cost of each song is a constant, denoted as c. Therefore, the remaining balance after purchasing x songs can be represented as:
y = 20 - cx
Understanding the Equation
The equation y = 20 - cx represents the relationship between the remaining balance (y) and the number of songs purchased (x). The initial balance of the gift card is $20, and the remaining balance decreases by the cost of each song (c). When x = 0, the remaining balance is equal to the initial balance, which is $20. As x increases, the remaining balance decreases, and when x = 16, the remaining balance is $0.
Example Use Case
Let's consider an example use case to illustrate the application of the equation. Suppose Renata wants to know how many songs she can purchase with a remaining balance of $10. We can use the equation y = 20 - cx to solve for x:
10 = 20 - cx
Subtracting 20 from both sides gives:
-10 = -cx
Dividing both sides by -c gives:
x = 10/c
Since the cost of each song is $1, we can substitute c = 1 into the equation:
x = 10/1
x = 10
Therefore, Renata can purchase 10 songs with a remaining balance of $10.
Conclusion
In conclusion, the equation y = 20 - cx represents the relationship between the remaining balance (y) and the number of songs purchased (x). The initial balance of the gift card is $20, and the remaining balance decreases by the cost of each song (c). This equation can be used to determine the number of songs that can be purchased with a given remaining balance. By understanding this relationship, Renata can make informed decisions about her music purchases and maximize the value of her gift card.
References
- [1] Algebraic equations
- [2] Gift card balance
- [3] Music purchases
Further Reading
- [1] Understanding algebraic equations
- [2] Gift card balance management
- [3] Music purchasing strategies
Frequently Asked Questions About Gift Card Balance and Music Purchases
Introduction
In our previous article, we explored the relationship between the remaining balance on a gift card and the number of songs purchased. We derived an equation that accurately represents this relationship and provided an example use case to illustrate its application. In this article, we will address some frequently asked questions about gift card balance and music purchases.
Q&A
Q: What is the initial balance of the gift card?
A: The initial balance of the gift card is $20.
Q: How does the remaining balance decrease as I purchase songs?
A: The remaining balance decreases by the cost of each song (c). As you purchase more songs, the remaining balance decreases accordingly.
Q: Can I use the equation to determine the number of songs I can purchase with a given remaining balance?
A: Yes, you can use the equation y = 20 - cx to solve for x, which represents the number of songs you can purchase with a given remaining balance.
Q: What if the cost of each song is not $1?
A: If the cost of each song is not $1, you can substitute the actual cost (c) into the equation to determine the number of songs you can purchase with a given remaining balance.
Q: Can I use the equation to determine the remaining balance after purchasing a certain number of songs?
A: Yes, you can use the equation y = 20 - cx to determine the remaining balance after purchasing a certain number of songs.
Q: What if I want to purchase songs with a remaining balance of $10?
A: You can use the equation y = 20 - cx to solve for x, which represents the number of songs you can purchase with a remaining balance of $10.
Q: Can I use the equation to determine the number of songs I can purchase with a remaining balance of $5?
A: Yes, you can use the equation y = 20 - cx to solve for x, which represents the number of songs you can purchase with a remaining balance of $5.
Example Use Cases
- Suppose you want to know how many songs you can purchase with a remaining balance of $15. You can use the equation y = 20 - cx to solve for x: 15 = 20 - cx Subtracting 20 from both sides gives: -5 = -cx Dividing both sides by -c gives: x = 5/c Since the cost of each song is $1, you can substitute c = 1 into the equation: x = 5/1 x = 5 Therefore, you can purchase 5 songs with a remaining balance of $15.
- Suppose you want to know how many songs you can purchase with a remaining balance of $20. You can use the equation y = 20 - cx to solve for x: 20 = 20 - cx Subtracting 20 from both sides gives: 0 = -cx Dividing both sides by -c gives: x = 0/c Since the cost of each song is $1, you can substitute c = 1 into the equation: x = 0/1 x = 0 Therefore, you cannot purchase any songs with a remaining balance of $20.
Conclusion
In conclusion, the equation y = 20 - cx represents the relationship between the remaining balance (y) and the number of songs purchased (x). This equation can be used to determine the number of songs that can be purchased with a given remaining balance. By understanding this relationship, you can make informed decisions about your music purchases and maximize the value of your gift card.
References
- [1] Algebraic equations
- [2] Gift card balance
- [3] Music purchases
Further Reading
- [1] Understanding algebraic equations
- [2] Gift card balance management
- [3] Music purchasing strategies