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 \[ = {\text{Rs}}{\text{.}}\dfrac{y}{2}\]
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 \[y\].