Solving a System of Equations to Determine the Cost of Pencils and Erasers

Whether you are a student or a small business owner, understanding how to solve a system of equations can be crucial. In this article, we will walk through a practical example where we need to determine the individual costs of pencils and erasers. Let's break down the problem and see how we can solve it step by step.

Problem Statement

The problem gives us the following two equations:

5 pencils and 3 erasers cost 27:

5P 3E 27 …… (equation a)

2 pencils and 4 erasers cost 22:

2P 4E 22 …… (equation b)

Step-by-Step Solution

Step 1: Add the Two Equations Together

We start by adding the two equations to eliminate the constants (27 and 22) and create a new equation:

(5P 3E) (2P 4E) 27 22

7P 7E 49

Step 2: Simplify the Equation

Now we can simplify the equation by dividing all terms by 7:

P E 7

Step 3: Interpret the Result

The equation P E 7 tells us that the combined cost of one pencil and one eraser is 7 units (the units could be dollars, cents, or any other currency).

Conclusion

Therefore, the cost of 1 pencil and 1 eraser together is 7 units.

Conclusion

By solving this system of equations, we have determined that the individual cost of a pencil and an eraser combined is 7 units. This methodology can be applied to other similar problems where you need to find the values of multiple variables from a set of linear equations.

Related Keywords

Keywords: system of equations, algebra, cost calculation, solving equations