Rosa Brought $d$ Drawings To An Art Show. After Selling 14 Of Them, She Had 34 Left. Identify The Equation That Represents This Situation And The Correct Solution.A. $d + 14 = 34 ; D = 20$ B. $d - 14 = 34 ; D = 48$ C.
Introduction
In this problem, we are given a scenario where Rosa brings a certain number of drawings to an art show and sells 14 of them, leaving her with 34 drawings. We need to identify the equation that represents this situation and find the correct solution for the number of drawings Rosa initially brought to the art show.
Understanding the Problem
Let's break down the problem step by step:
- Rosa brings d drawings to the art show.
- She sells 14 of them, which means she is left with d - 14 drawings.
- After selling 14 drawings, Rosa has 34 drawings left.
We can represent this situation using an equation. Let's start by identifying the key elements:
- The initial number of drawings Rosa brings to the art show is d.
- The number of drawings she sells is 14.
- The number of drawings she has left after selling 14 is 34.
Identifying the Equation
Based on the information above, we can write an equation to represent the situation:
d - 14 = 34
This equation states that the number of drawings Rosa has left after selling 14 is equal to 34.
Solving the Equation
To solve for d, we need to isolate the variable d on one side of the equation. We can do this by adding 14 to both sides of the equation:
d - 14 + 14 = 34 + 14
This simplifies to:
d = 48
Therefore, the correct solution is d = 48.
Conclusion
In this problem, we identified the equation that represents the situation where Rosa brings a certain number of drawings to an art show and sells 14 of them, leaving her with 34 drawings. We then solved the equation to find the correct solution for the number of drawings Rosa initially brought to the art show.
Answer
The correct answer is:
B.
Discussion
This problem is a classic example of a linear equation in one variable. The equation d - 14 = 34 represents a linear relationship between the number of drawings Rosa brings to the art show and the number of drawings she has left after selling 14.
The solution to the equation, d = 48, represents the initial number of drawings Rosa brought to the art show. This solution can be verified by plugging it back into the original equation:
48 - 14 = 34
This confirms that the solution is correct.
Tips and Variations
This problem can be modified in various ways to make it more challenging or interesting. For example:
- What if Rosa sells 20 drawings instead of 14?
- What if Rosa has 50 drawings left after selling 14?
- What if Rosa brings 60 drawings to the art show?
These variations can be used to create more complex equations and solutions, or to explore different scenarios and applications of linear equations.
Real-World Applications
Linear equations like this one have many real-world applications, such as:
- Modeling population growth or decline
- Representing financial transactions or budgets
- Describing physical systems or processes
Q: What is the equation that represents the situation where Rosa brings a certain number of drawings to an art show and sells 14 of them, leaving her with 34 drawings?
A: The equation that represents this situation is d - 14 = 34, where d is the initial number of drawings Rosa brings to the art show.
Q: How do I solve the equation to find the correct solution for the number of drawings Rosa initially brought to the art show?
A: To solve the equation, you need to isolate the variable d on one side of the equation. You can do this by adding 14 to both sides of the equation:
d - 14 + 14 = 34 + 14
This simplifies to:
d = 48
Q: What if Rosa sells 20 drawings instead of 14? How would I represent this situation mathematically?
A: If Rosa sells 20 drawings instead of 14, you would represent this situation mathematically by changing the equation to:
d - 20 = 34
To solve for d, you would add 20 to both sides of the equation:
d - 20 + 20 = 34 + 20
This simplifies to:
d = 54
Q: What if Rosa has 50 drawings left after selling 14? How would I represent this situation mathematically?
A: If Rosa has 50 drawings left after selling 14, you would represent this situation mathematically by changing the equation to:
d - 14 = 50
To solve for d, you would add 14 to both sides of the equation:
d - 14 + 14 = 50 + 14
This simplifies to:
d = 64
Q: What if Rosa brings 60 drawings to the art show? How would I represent this situation mathematically?
A: If Rosa brings 60 drawings to the art show, you would represent this situation mathematically by changing the equation to:
d - 14 = 34
However, since Rosa brings 60 drawings to the art show, you would need to change the equation to:
60 - 14 = 34
This is already true, so the equation is satisfied.
Q: What are some real-world applications of linear equations like this one?
A: Linear equations like this one have many real-world applications, such as:
- Modeling population growth or decline
- Representing financial transactions or budgets
- Describing physical systems or processes
By understanding and solving linear equations like this one, you can develop problem-solving skills and apply mathematical concepts to real-world situations.
Q: How can I use this problem to create more complex equations and solutions?
A: You can modify this problem in various ways to create more complex equations and solutions, such as:
- Changing the number of drawings Rosa sells or has left
- Changing the initial number of drawings Rosa brings to the art show
- Adding more variables or constraints to the problem
By experimenting with different variations of this problem, you can develop your problem-solving skills and apply mathematical concepts to a wide range of situations.