Question

Form the pair of the linear equation from the following information: Sachin tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.”

Answer 1

Hint: Assume that the present age of Sachin be x years and his daughter be y years old.
The age of Sachin and Sachin’s daughter before seven years is \[\left( x-7 \right)\] and \[\left( y-7 \right)\] . It is given that the age of Sachin is seven times more than his daughter’s age. Use this information and form an equation. The age of Sachin and Sachin’s daughter after three years is \[\left( x+3 \right)\] and \[\left( y+3 \right)\] . It is given that the age of Sachin is three times more than his daughter’s age. Use this information and form another equation. Now, we have the required pair of linear equations.

Complete step-by-step answer:
According to the question, it is given that Sachin tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.”
First of all, let us assume that the present age of Sachin be x years and his daughter be y years old.
The present age of Sachin = x years …………………………(1)
The present age of Sachin's daughter = y years …………………………(2)
In \[{{1}^{st}}\] case, it is given that
Seven years ago, Sachin was seven times as old as his daughter was then.
The age of Sachin before seven years = \[\left( x-7 \right)\] years …………………………..(3)
The age of Sachin’s daughter before seven years = \[\left( y-7 \right)\] years ……………………………….(4)
We have that the age of Sachin is seven times more than his daughter’s age. So,
\[\left( x-7 \right)=7\left( y-7 \right)\] ………………………………..(5)
In \[{{2}^{nd}}\] case, it is given that
Three years from now, Sachin will be three times as old as his daughter will be then.
The age of Sachin before after three years = \[\left( x+3 \right)\] years …………………………..(6)
The age of Sachin’s daughter after three years = \[\left( y+3 \right)\] years ……………………………….(7)
We have that the age of Sachin is three times more than his daughter’s age. So,
\[\left( x+3 \right)=3\left( y+3 \right)\] ………………………………..(8)
From equation (5) and equation (8), we have two linear equations in terms of \[x\] and \[y\] .
Hence, the pair of linear equations for the given information are \[\left( x-7 \right)=7\left( y-7 \right)\] and \[\left( x+3 \right)=3\left( y+3 \right)\] .

Note: In this question, one might make a silly mistake while forming the linear equation for the statement “Seven years ago, Sachin was seven times as old as his daughter was then”. One might make the equation as \[7\left( x-7 \right)=\left( y-7 \right)\] . This is wrong because the age of Sachin is already 7 times of his daughter. So, to make the age of Sachin and his daughter’ age equal, we have to multiply by 7 in the age of his daughter. SO, the correct equation is \[\left( x-7 \right)=7\left( y-7 \right)\] .