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: We can take the cost of ball pen as one variable and cost of fountain pen as another variable. By reading the given statement, we can understand that half of the cost of a fountain pen minus 5 gives the cost of a ball pen. We get the required equation by writing the relation in terms to two variables and simplifying.

Complete step by step answer:

We are given two objects, a ball pen and fountain pen. We can assign any two variables to the cost of ball pen and cost of fountain pen
Let $$\text{x = }$$ cost of fountain pen
And let $$\text{y = }$$ cost of ball pen
According to the question, half of the cost of fountain pen minus 5 gives the cost of a ball pen. Writing this in terms of variables, we get,
$\text{y = }{\displaystyle \frac{\text{x}}{\text{2}}}\text{ - 5}$
Rearranging the equation, we get
$$\begin{gathered} \text{y + 5 = }{\displaystyle \frac{\text{x}}{\text{2}}} \\ \text{2y + 10 = x} \end{gathered}$$
Therefore, the required linear equation in 2 variables is $\text{x = 2y + 10}$.

Note: As the variable is not mentioned, we can use any variable. We must make sure that it is clearly written what each of the variables used refers to, and we should not mix them up. In this problem we convert a statement into a mathematical equation. This method of solving is known as mathematical modeling. Using mathematical modeling we can form equations from a statement and we can solve for the variable if the number of equations formed is greater than the number of variables, we can solve for the variables. The number of variables used must be minimum to avoid errors. We must read and understand the given statement completely to form the equations.