**Question:** Aftab 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.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Solution:

Let the present age of Aftab be ‘x’.

And, the present age of his daughter be ‘y’.

Now, we can write, seven years ago,

Age of Aftab = x – 7

Age of his daughter = y – 7

According to the question,

x−7 = 7(y−7)

⇒ x−7 = 7y−49

⇒ x−7y = −42 ………………………(i)

Also, three years from now or after three years,

Age of Aftab will become = x + 3.

Age of his daughter will become = y + 3

According to the situation given,

x+3 = 3(y+3)

⇒x+3 = 3y+9

⇒x−3y = 6 …………..…………………(ii)

Subtracting equation (i) from equation (ii) we have

(x−3y)−(x−7y) = 6−(−42)

⇒−3y+7y=6+42

⇒4y=48

⇒y=12

The algebraic equation is represented by

x−7y = −42

x−3y = 6

For, x−7y =−42 or x = −42+7y

The solution table is

For, x−3y=6 or x=6+3y

The solution table is

The graphical representation is:

Class | 10th |

Subject | Maths |

Chapter | Pair of Linear Equations in Two Variables |

Exercise | 3.1 |

Next Question | The coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later, she buys another bat and 3 more balls of the same kind for Rs.1300. Represent this situation algebraically and geometrically. |