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.

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.

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 $= {\text{Rs}}{\text{.}}\dfrac{y}{2}$
Since the cost of ball pen is Rs.5 less than half of the cost of fountain pen we have
$\Rightarrow {\text{Rs}}{\text{.}}x = {\text{Rs}}{\text{.}}\dfrac{y}{2} - {\text{Rs}}{\text{.5}} \\ \Rightarrow x = \dfrac{y}{2} - 5 \\$
By multiplying both sides with 2, we have
$\Rightarrow 2x = 2\left( {\dfrac{y}{2} - 5} \right) \\ \Rightarrow 2x = y - 2 \times 5 \\ \Rightarrow 2x = y - 10 \\ \therefore 2x - y + 10 = 0 \\$
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 $y$.