Question

Ravish tells his daughter Aarushi, ''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''. If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically.

Answer 1

We are given the present age of Ravish as y years and Aarushi as x years.

Age of Ravish seven years ago

Age of Aarushi seven years ago

It has already been said by Ravish that seven years ago he was seven times old then Aarushi was then

So,

Age of Ravish three years from now

Age of Aarushi three years from now

It has already been said by Ravish that three years from now he will be three times old then Aarushi will be then

So,

(1) and (2) are the algebraic representation of the given statement.

We are given,

We get,

Now, substituting in ,we get

Substituting in, we get

Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the given equation

x	0	6
y	–42	0

We are given,

We get,

Now, substituting in ,we get

Substituting in ,we get

Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the given equation

x	0	–2
y	6	0

The red -line represents the equation.

The blue-line represents the equation.