Question

The cost of a ball pen is Rs 5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.

Answer 1

Hint:
Let the cost of the fountain pen as $x$ and cost of the ball pen be $y$. Then, form the equation according to the given condition. The equation can also be written by rearranging the terms.

Complete step by step solution:
Let the cost of the fountain pen as $x$ and cost of ball pen be $y$
Then, we are given that the cost of a ball pen is 5 less than half the cost of a fountain pen.
Then, according to the given statement, we can write it mathematically as,
$y={\displaystyle \frac{x}{2}}-5$
Here, the equation is linear as the maximum power of the variable is 1 and there are two variables, $x$ and $y$.
Therefore, the equation is a linear equation in two variables.
The equation can be rearranged as
$$\begin{gathered} 2y=x-10 \\ \Rightarrow x-2y=10 \end{gathered}$$

Thus, the required equation is $x-2y=10$, where $x$ is the cost of a fountain pen and the $y$ is the cost of a ball pen.

Note:
We can use any variables for the cost of fountain pen and cost pen. After labelling the variables, the formation of the equation should be correct. There can be more equivalent equations depending on the position of variables in the equation. For example, $2y=x-10$ is equivalent to $x-2y=10$.