3) Nine Pens Cost Rs. 4. How Many Pens Can Be Purchased For Rs. 4032?Given:- 9 Pens Cost Rs. 4- Amount Available: Rs. 4032To Find The Number Of Pens $x$ For Rs. 4032:Set Up The Proportion:$\[ \frac{9}{4} = \frac{x}{4032} \\]Solve

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Solving the Puzzle: Nine Pens for Rs. 4032

In this article, we will delve into a simple yet intriguing problem that involves basic algebra and proportion. The problem states that nine pens cost Rs. 4, and we need to find out how many pens can be purchased for Rs. 4032. This problem is a great example of how math can be applied to real-life scenarios, and it requires us to set up a proportion and solve for the unknown variable.

Setting Up the Proportion

To solve this problem, we need to set up a proportion that relates the number of pens to the cost. The proportion is set up as follows:

{ \frac{9}{4} = \frac{x}{4032} \}

In this proportion, the left-hand side represents the number of pens (9) and the cost (Rs. 4), while the right-hand side represents the unknown number of pens (x) and the available amount (Rs. 4032).

Solving the Proportion

To solve for x, we can cross-multiply the proportion:

{ 9 \times 4032 = 4 \times x \}

This simplifies to:

{ 36288 = 4x \}

Now, we can divide both sides by 4 to solve for x:

{ x = \frac{36288}{4} \}

Calculating the Number of Pens

Now that we have the equation, we can calculate the number of pens that can be purchased for Rs. 4032:

{ x = \frac{36288}{4} \}

x = 9072

Therefore, 9072 pens can be purchased for Rs. 4032.

In this article, we have solved a simple yet intriguing problem that involves basic algebra and proportion. We set up a proportion and solved for the unknown variable, which represents the number of pens that can be purchased for Rs. 4032. This problem is a great example of how math can be applied to real-life scenarios, and it requires us to think critically and solve problems step by step.

Real-World Applications

This problem has several real-world applications, such as:

  • Shopping: When shopping for pens or other items, we need to consider the cost and the number of items we can purchase.
  • Budgeting: When creating a budget, we need to consider the cost of items and the number of items we can purchase within our budget.
  • Mathematical Modeling: This problem can be used to model real-world scenarios, such as calculating the cost of items or the number of items that can be purchased within a certain budget.

Tips and Tricks

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

  • Read the problem carefully: Make sure you understand the problem and what is being asked.
  • Set up a proportion: Use a proportion to relate the number of pens to the cost.
  • Solve for the unknown variable: Use algebra to solve for the unknown variable, which represents the number of pens that can be purchased.
  • Check your answer: Make sure your answer is reasonable and makes sense in the context of the problem.

Frequently Asked Questions

Here are some frequently asked questions about this problem:

  • What is the cost of one pen?
    • The cost of one pen is Rs. 4/9.
  • How many pens can be purchased for Rs. 4032?
    • 9072 pens can be purchased for Rs. 4032.
  • What is the proportion used to solve this problem?
    • The proportion is ${ \frac{9}{4} = \frac{x}{4032} }$
      Q&A: Solving the Puzzle of Nine Pens for Rs. 4032

In our previous article, we solved the puzzle of nine pens for Rs. 4032 by setting up a proportion and solving for the unknown variable. In this article, we will answer some frequently asked questions about this problem and provide additional insights and tips.

Q: What is the cost of one pen?

A: The cost of one pen is Rs. 4/9.

Q: How many pens can be purchased for Rs. 4032?

A: 9072 pens can be purchased for Rs. 4032.

Q: What is the proportion used to solve this problem?

A: The proportion is ${ \frac{9}{4} = \frac{x}{4032} }$

Q: How do I set up a proportion to solve this problem?

A: To set up a proportion, you need to relate the number of pens to the cost. In this case, the proportion is ${ \frac{9}{4} = \frac{x}{4032} }$. This means that the ratio of 9 pens to Rs. 4 is equal to the ratio of x pens to Rs. 4032.

Q: How do I solve for the unknown variable?

A: To solve for the unknown variable, you need to use algebra to isolate the variable. In this case, you can cross-multiply the proportion and then divide both sides by 4 to solve for x.

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

A: This problem has several real-world applications, such as:

  • Shopping: When shopping for pens or other items, you need to consider the cost and the number of items you can purchase.
  • Budgeting: When creating a budget, you need to consider the cost of items and the number of items you can purchase within your budget.
  • Mathematical Modeling: This problem can be used to model real-world scenarios, such as calculating the cost of items or the number of items that can be purchased within a certain budget.

Tips and Tricks

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

  • Read the problem carefully: Make sure you understand the problem and what is being asked.
  • Set up a proportion: Use a proportion to relate the number of pens to the cost.
  • Solve for the unknown variable: Use algebra to solve for the unknown variable, which represents the number of pens that can be purchased.
  • Check your answer: Make sure your answer is reasonable and makes sense in the context of the problem.

Common Mistakes

Here are some common mistakes to avoid when solving this problem:

  • Not reading the problem carefully: Make sure you understand the problem and what is being asked.
  • Not setting up a proportion: Use a proportion to relate the number of pens to the cost.
  • Not solving for the unknown variable: Use algebra to solve for the unknown variable, which represents the number of pens that can be purchased.
  • Not checking your answer: Make sure your answer is reasonable and makes sense in the context of the problem.

In this article, we have answered some frequently asked questions about the problem of nine pens for Rs. 4032 and provided additional insights and tips. We hope this article has been helpful in understanding the problem and how to solve it. If you have any further questions or need additional help, please don't hesitate to ask.