Solving for the Cost of Markers and Erasers: A System of Equations Approach

When dealing with real-world scenarios involving multiple variables, such as the cost of pencils, paper, or markers, we often turn to the power of algebra. In this article, we will explore a practical problem involving markers and erasers and solve it step-by-step using a system of equations. This method is not only useful for academic purposes but also applicable in various real-life situations where cost calculations are necessary.

Introduction to the Problem

Consider the following problem: Two markers and one eraser cost 35 pesos, and three markers and four erasers cost 65 pesos. What is the cost of a marker and an eraser?

Setting Up the Equations

Let's define the variables first. We will let:

Cost of 1 marker M Cost of 1 eraser E

Based on the given problem, we can set up the following equations:

2M E 35 3M 4E 65

Solving the System of Equations

To solve for M and E, we will use the method of elimination. Let's start by eliminating one of the variables.

Step 1: Multiply the equations to align coefficients

Multiply the first equation by 3 and the second equation by 2:

3(2M E) 3(35) 6M 3E 105 2(3M 4E) 2(65) 6M 8E 130

Step 2: Subtract the first modified equation from the second

Subtract the first modified equation from the second to eliminate M:

6M 8E - (6M 3E) 130 - 105

Simplifying this, we get:

5E 25

Therefore:

E 5

Step 3: Substitute the value of E back into one of the original equations

Substitute E 5 into the first original equation:

2M 5 35

Solving for M:

2M 35 - 5

2M 30

M 15

Verifying the Solution

Let's verify if our solution satisfies both original equations:

2M E 2(15) 5 30 5 35 3M 4E 3(15) 4(5) 45 20 65

Conclusion

The solution to the problem is that the cost of one marker is 15 pesos, and the cost of one eraser is 5 pesos. This method of solving systems of equations is a powerful tool in various fields, including finance, economics, and engineering, making it essential to understand and master.

By applying algebraic techniques, we can solve complex problems and make informed decisions in our daily lives and professional careers.

Keywords

system of equations, algebraic solution, cost calculation