Cost of a pen is two and half times the cost of a pencil. Express this situation as alinear equation in two variables

1. Break Down the Problem

To express the situation as a linear equation in two variables, we need to identify the variables involved and their relationship.

Let:

• $p$ = cost of a pencil
• $c$ = cost of a pen

According to the problem, the cost of a pen is two and half times the cost of a pencil. This translates to a mathematical expression.

2. Relevant Concepts

The phrase "two and half times" can be expressed as a multiplication factor. Two and a half is equal to $\frac{5}{2}$. Therefore, we can represent the relationship as:

$c = \frac{5}{2} p$

3. Analysis and Detail

In this equation:

• The left side ($c$) represents the cost of the pen.
• The right side ($\frac{5}{2} p$) indicates that the cost of the pen is $2.5$ times the cost of the pencil.

This equation describes a linear relationship between the cost of the pen and the pencil.

4. Verify and Summarize

The relationship we derived, $c = \frac{5}{2} p$, correctly models the situation described in the problem.

Final Answer

The linear equation representing the situation is:

$c = \frac{5}{2} p$