Question

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

Answer 1

Hint: In this question, we will proceed by considering the costs of a ball pen and a fountain pen as variables. Then find the half price of the fountain pen and use the given condition to require a linear equation in two variables.

Complete step-by-step answer:
Given that the cost of a ball pen is Rs.5 less than half of the cost of fountain pen.
Let the cost of a ball pen $$=\text{Rs}\text{.}x$$
And the cost of a fountain pen $$=\text{Rs}\text{.}y$$
So, half of cost of the fountain pen $$=\text{Rs}\text{.}{\displaystyle \frac{y}{2}}$$
Since the cost of ball pen is Rs.5 less than half of the cost of fountain pen we have
$$\begin{gathered} \Rightarrow \text{Rs}\text{.}x=\text{Rs}\text{.}{\displaystyle \frac{y}{2}}-\text{Rs}\text{.5} \\ \Rightarrow x={\displaystyle \frac{y}{2}}-5 \end{gathered}$$
By multiplying both sides with 2, we have
$$\begin{gathered} \Rightarrow 2x=2\left({\displaystyle \frac{y}{2}}-5\right) \\ \Rightarrow 2x=y-2\times 5 \\ \Rightarrow 2x=y-10 \\ \therefore 2x-y+10=0 \end{gathered}$$
Thus, the required equation in two variables is $$2x-y+10=0$$.

Note: Linear equation in two variables is an equation having two variables with degree one. For example, if $$a,b,r$$ are real numbers (and if $$a$$ and $$b$$ are not both equal to zero) then $$ax+by=r$$ is called a linear equation in two variables where variables are $$x$$ and $$y$$.