Question

Five years ago, Nuri was thrice as old as Sonu. Express the information in a linear equation.

Answer 1

Hint: Here we are given a statement regarding ages of Nuri and Sonu five years ago. We need to form a linear equation using this statement. For this, we will first suppose ages of Nuri and Sonu as some variables x and y respectively. Then we will find their ages 5 years ago by subtracting 5 from x and y. After that, we will use a statement to form an equation which will be required to be a linear equation.

Complete step-by-step answer:
Let us suppose present ages of Nuri and Sonu as x and y respectively. Therefore,
Present age of Nuri = x years.
Present age of Sonu = y years.
Now, let us find their ages 5 years ago, so we need to subtract 5 from their present age. Hence, we get:
Age of Nuri 5 years ago = (x-5) years.
Age of Sonu 5 years ago = (y-5) years.
As we are given that, 5 years ago, Nuri was thrice as old as Sonu. Hence, (y-5) is thrice of (x-5).
Expressing it into an equation we get:
$y-5=3\left( x-5 \right)$.
Simplifying the right side of the equation, we get:
$y-5=3x-15$.
Taking variables on one side and constant on the other side we get:
$y-3x=-15+5\Rightarrow y-3x=-10$.
Let us make the constant as positive. So taking negative signs common from the left side and cancelling with negative signs of the right side of the equation, we get: $3x-y=10$.
Hence, this is our required equation. Since degrees of x and y both are 1, so it is a linear equation.

Note: Students should take care while changing word problems into equations. Taking proper variables for proper terms is important. Here, students usually make the mistake of multiplying 3 by (y-5) rather than (x-5). They should check the degree of the equation to make sure that it is a linear equation.