Select The Correct Answer.Jonathan Collects Postcards And Stamps. The Number Of Postcards In His Collection Is 12 More Than $ \frac{3}{4} $ The Number Of Stamps. He Has 39 Postcards In All. If Jonathan Has $ X $ Stamps, Which Equation

Introduction

In this problem, we are given information about Jonathan's postcard and stamp collection. We know that the number of postcards in his collection is 12 more than $\frac{3}{4}$ the number of stamps. We are also given that Jonathan has a total of 39 postcards. Our goal is to find the number of stamps, denoted by $x$, that Jonathan has in his collection.

Step 1: Understand the Problem

Let's start by understanding the problem. We are given that the number of postcards in Jonathan's collection is 12 more than $\frac{3}{4}$ the number of stamps. This can be represented as:

$$\text{Number of postcards} = \frac{3}{4} \times \text{Number of stamps} + 12$$

We are also given that Jonathan has a total of 39 postcards. This can be represented as:

$$\text{Number of postcards} = 39$$

Step 2: Write an Equation

Now that we have understood the problem, let's write an equation to represent the situation. We know that the number of postcards is 12 more than $\frac{3}{4}$ the number of stamps. This can be represented as:

$$\frac{3}{4}x + 12 = 39$$

where $x$ is the number of stamps.

Step 3: Solve the Equation

To solve the equation, we need to isolate the variable $x$. We can do this by subtracting 12 from both sides of the equation:

$$\frac{3}{4}x = 27$$

Next, we can multiply both sides of the equation by $\frac{4}{3}$ to get:

$$x = 36$$

Conclusion

Therefore, Jonathan has 36 stamps in his collection.

The Correct Equation

The correct equation to represent the situation is:

$$\frac{3}{4}x + 12 = 39$$

This equation represents the relationship between the number of postcards and the number of stamps in Jonathan's collection.

Why is this Equation Correct?

This equation is correct because it accurately represents the relationship between the number of postcards and the number of stamps in Jonathan's collection. The equation states that the number of postcards is 12 more than $\frac{3}{4}$ the number of stamps, which is consistent with the information given in the problem.

What is the Significance of this Equation?

The significance of this equation is that it allows us to determine the number of stamps in Jonathan's collection. By solving the equation, we can find the value of $x$, which represents the number of stamps.

How to Use this Equation

To use this equation, we need to substitute the value of the number of postcards into the equation. In this case, we know that Jonathan has 39 postcards, so we can substitute 39 for the number of postcards in the equation:

$$\frac{3}{4}x + 12 = 39$$

By solving this equation, we can find the value of $x$, which represents the number of stamps in Jonathan's collection.

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

• Make sure to read the problem carefully and understand what is being asked.
• Use variables to represent the unknown quantities in the problem.
• Write an equation to represent the relationship between the variables.
• Solve the equation to find the value of the variable.
• Check your answer to make sure it is consistent with the information given in the problem.

Conclusion

In conclusion, the correct equation to represent the situation is:

$$\frac{3}{4}x + 12 = 39$$

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Q: What is the relationship between the number of postcards and the number of stamps in Jonathan's collection?

A: The number of postcards in Jonathan's collection is 12 more than $\frac{3}{4}$ the number of stamps.

Q: How can we represent this relationship mathematically?

A: We can represent this relationship mathematically using the equation:

$$\frac{3}{4}x + 12 = 39$$

where $x$ is the number of stamps.

Q: How do we solve the equation to find the value of $x$?

A: To solve the equation, we need to isolate the variable $x$. We can do this by subtracting 12 from both sides of the equation:

$$\frac{3}{4}x = 27$$

Next, we can multiply both sides of the equation by $\frac{4}{3}$ to get:

$$x = 36$$

Q: What is the significance of the value of $x$?

A: The value of $x$ represents the number of stamps in Jonathan's collection.

Q: How can we use this equation to solve similar problems?

A: We can use this equation to solve similar problems by substituting the value of the number of postcards into the equation and solving for the value of $x$.

Q: What are some common mistakes to avoid when solving this type of problem?

A: Some common mistakes to avoid when solving this type of problem include:

• Not reading the problem carefully and understanding what is being asked.
• Not using variables to represent the unknown quantities in the problem.
• Not writing an equation to represent the relationship between the variables.
• Not solving the equation to find the value of the variable.
• Not checking the answer to make sure it is consistent with the information given in the problem.

Q: How can we check our answer to make sure it is correct?

A: We can check our answer by substituting the value of $x$ back into the original equation and making sure it is true.

Q: What are some real-world applications of this type of problem?

A: Some real-world applications of this type of problem include:

• Calculating the number of items in a collection based on the number of items of a different type.
• Determining the cost of an item based on the cost of a related item.
• Finding the number of people in a group based on the number of people in a related group.

Q: How can we extend this problem to include more variables and complexity?

A: We can extend this problem to include more variables and complexity by adding more equations and variables to the problem. For example, we could add an equation that represents the relationship between the number of postcards and the number of stamps, and another equation that represents the relationship between the number of stamps and the number of other items in the collection.

Q: What are some tips and tricks for solving this type of problem?

A: Some tips and tricks for solving this type of problem include:

• Reading the problem carefully and understanding what is being asked.
• Using variables to represent the unknown quantities in the problem.
• Writing an equation to represent the relationship between the variables.
• Solving the equation to find the value of the variable.
• Checking the answer to make sure it is consistent with the information given in the problem.

Conclusion

In conclusion, the correct equation to represent the situation is:

$$\frac{3}{4}x + 12 = 39$$

This equation represents the relationship between the number of postcards and the number of stamps in Jonathan's collection. By solving this equation, we can find the value of $x$, which represents the number of stamps in Jonathan's collection.