Together, Matthew And Daniel Have 67 DVDs. Matthew's Collection Has 3 Times As Many DVDs As Daniel's Collection. Which Equation Can Be Used To Determine The Number Of DVDs In Daniel's Collection?A. 3 X − X = 67 3x - X = 67 3 X − X = 67 B. X + X = 67 X + X = 67 X + X = 67 C.
Introduction
In this article, we will delve into the world of mathematics and explore a problem that involves algebraic equations. We will examine a scenario where two individuals, Matthew and Daniel, have a combined collection of 67 DVDs. The problem states that Matthew's collection has 3 times as many DVDs as Daniel's collection. Our goal is to determine the number of DVDs in Daniel's collection using an equation.
Understanding the Problem
Let's break down the information provided in the problem:
- Matthew and Daniel have a combined collection of 67 DVDs.
- Matthew's collection has 3 times as many DVDs as Daniel's collection.
We can represent the number of DVDs in Daniel's collection as "x". Since Matthew's collection has 3 times as many DVDs as Daniel's collection, we can represent the number of DVDs in Matthew's collection as "3x".
Formulating the Equation
Now that we have represented the number of DVDs in both collections, we can formulate an equation to determine the number of DVDs in Daniel's collection. The equation should represent the total number of DVDs in both collections, which is 67.
We can write the equation as:
3x + x = 67
This equation represents the total number of DVDs in both collections. The left-hand side of the equation represents the sum of the number of DVDs in Matthew's collection (3x) and the number of DVDs in Daniel's collection (x). The right-hand side of the equation represents the total number of DVDs, which is 67.
Simplifying the Equation
To simplify the equation, we can combine like terms on the left-hand side:
4x = 67
This equation is now in a simpler form, and we can solve for x to determine the number of DVDs in Daniel's collection.
Solving for x
To solve for x, we can divide both sides of the equation by 4:
x = 67/4
x = 16.75
Since we cannot have a fraction of a DVD, we can round down to the nearest whole number. However, in this case, we are looking for an equation that represents the number of DVDs in Daniel's collection, not the actual number of DVDs.
Conclusion
In conclusion, the equation that can be used to determine the number of DVDs in Daniel's collection is:
4x = 67
This equation represents the total number of DVDs in both collections and can be used to solve for x, which represents the number of DVDs in Daniel's collection.
Answer
The correct answer is:
C. 4x = 67
Introduction
In our previous article, we explored a problem that involved algebraic equations and determined the equation that can be used to determine the number of DVDs in Daniel's collection. In this article, we will provide a Q&A section to further clarify the concepts and provide additional insights.
Q&A
Q: What is the main concept behind the equation 4x = 67?
A: The main concept behind the equation 4x = 67 is that it represents the total number of DVDs in both Matthew's and Daniel's collections. The left-hand side of the equation, 4x, represents the sum of the number of DVDs in Matthew's collection (3x) and the number of DVDs in Daniel's collection (x).
Q: Why is the equation 4x = 67 a correct representation of the problem?
A: The equation 4x = 67 is a correct representation of the problem because it takes into account the fact that Matthew's collection has 3 times as many DVDs as Daniel's collection. By combining the number of DVDs in both collections, we can determine the total number of DVDs, which is 67.
Q: Can we use the equation 3x - x = 67 to determine the number of DVDs in Daniel's collection?
A: No, we cannot use the equation 3x - x = 67 to determine the number of DVDs in Daniel's collection. This equation is incorrect because it represents the difference between the number of DVDs in Matthew's collection and the number of DVDs in Daniel's collection, rather than the sum.
Q: What is the significance of the number 4 in the equation 4x = 67?
A: The number 4 in the equation 4x = 67 represents the total number of times that the number of DVDs in Daniel's collection is added to the number of DVDs in Matthew's collection. Since Matthew's collection has 3 times as many DVDs as Daniel's collection, we need to add the number of DVDs in Daniel's collection (x) to the number of DVDs in Matthew's collection (3x), which results in a total of 4x.
Q: Can we use the equation x + x = 67 to determine the number of DVDs in Daniel's collection?
A: No, we cannot use the equation x + x = 67 to determine the number of DVDs in Daniel's collection. This equation is incorrect because it represents the sum of the number of DVDs in Daniel's collection, rather than the sum of the number of DVDs in both Matthew's and Daniel's collections.
Q: What is the final answer to the problem?
A: The final answer to the problem is the equation 4x = 67, which represents the total number of DVDs in both Matthew's and Daniel's collections.
Conclusion
In conclusion, the equation 4x = 67 is a correct representation of the problem and can be used to determine the number of DVDs in Daniel's collection. We hope that this Q&A section has provided additional insights and clarified any confusion. If you have any further questions, please don't hesitate to ask.
Answer
The correct answer is:
C. 4x = 67
This equation represents the total number of DVDs in both Matthew's and Daniel's collections and can be used to solve for x, which represents the number of DVDs in Daniel's collection.