Solving Math Word Problems: The Cost of a Pen and a Pencil

Mathematics often involves solving real-world problems through mathematical reasoning and concepts. This article delves into a simple yet intriguing problem: determining the individual costs of a pen and a pencil based on given conditions. We will solve this problem step-by-step, ensuring a clear understanding of the process.

Introduction to the Problem

The cost of a pen is 3 times the cost of a pencil. We need to find the cost of a pencil if the total cost of 4 pencils and 3 pens is $9.75. Let's denote the cost of a pencil as p (in dollars) and the cost of a pen as 3p.

Setting Up the Equation

Given the problem statement, we can set up the following equation based on the total cost of 4 pencils and 3 pens:

4p 3(3p) 9.75

Simplifying the equation:

4p 9p 9.75

Combining like terms:

13p 9.75

Solving for the Cost of a Pencil

To find the cost of a pencil, we divide both sides of the equation by 13:

p 9.75 / 13

P Calculating this, we get:

p 0.75

Therefore, the cost of a pencil is $0.75.

Verification of the Solution

Let's verify the solution by substituting the value of p back into the original conditions:

The cost of a pencil (p) is $0.75. The cost of a pen (3p) is 3 * $0.75 $2.25. The total cost of 4 pencils and 3 pens:

4 * $0.75 3 * $2.25 $3.00 $6.75 $9.75

This matches the given total cost, confirming our solution.

Additional Insights and Applications

This type of word problem is commonly encountered in various settings, such as:

Consumer behavior in retail. Cost analysis in business management. Financial planning for individuals and organizations.

Understanding how to solve such problems can greatly enhance one's problem-solving skills and analytical thinking abilities.

In conclusion, the cost of a pencil is $0.75, and the cost of a pen is $2.25, given the conditions provided in the problem.