Exploring the Relationship Between Rulers and Pencils: A Fun Math Problem

In the world of mathematics, there are many intriguing problems that can challenge our understanding and skills. One such problem involves the cost equivalence between rulers and pencils. The question posed is: If 4 rulers and 5 pencils equal the same cost as 2 rulers and 11 pencils, how many pencils can you buy for the same price as 5 rulers?

Understanding the Problem

To solve this problem, we need to establish an equation based on the given information. Let's denote the cost of one ruler as r and the cost of one pencil as p. The given condition can be written as:

4r 5p 2r 11p

Solving the Equation

Now, let's simplify and solve this equation step by step.

Step 1: Eliminate the Rulers

Subtract 2r from both sides of the equation: 4r 2r 11p 5p 2r 6p

Step 2: Solve for the Pencil Cost

Divide both sides by 2: r 3p

This tells us that the cost of one ruler is equivalent to the cost of three pencils.

Calculating the Number of Pencils for 5 Rulers

Now that we know the relationship between the cost of a ruler and a pencil, we can determine how many pencils can be bought for the same price as 5 rulers.

The cost of 5 rulers is: 5r 5(3p) 15p

To find out how many pencils can be bought for 15p:

15p / p 15

Therefore, you can buy 15 pencils for the same price as 5 rulers.

Conclusion

This problem is a great example of how basic algebra can be applied to real-world scenarios. It not only tests our understanding of mathematical concepts but also highlights the importance of logical reasoning. Understanding such relationships can also be useful in various fields, including economics and inventory management.

Further Exploration

Challenge yourself with similar problems or explore further by considering different quantities and costs. You can join our space to share more math problems and collaborate with fellow enthusiasts.

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