## EXERCISE 3.1

#### Page No 44:

#### Question 1:

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.

#### Answer:

Let the present age of Aftab be *x*.

And, present age of his daughter = *y*

Seven years ago,

Age of Aftab = *x* − 7

Age of his daughter = *y* − 7

According to the question,

Three years hence,

Age of Aftab = *x* + 3

Age of his daughter = *y* + 3

According to the question,

Therefore, the algebraic representation is

For ,

The solution table is

| − 7 | 0 | 7 |

| 5 | 6 | 7 |

For ,

The solution table is

| 6 | 3 | 0 |

| 0 | − 1 | − 2 |

The graphical representation is as follows.

#### Question 3:

The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.

#### Answer:

Let the cost of 1 kg of apples be Rs *x*.

And, cost of 1 kg of grapes = Rs *y*

According to the question, the algebraic representation is

For ,

The solution table is

| 50 | 60 | 70 |

| 60 | 40 | 20 |

For 4*x* + 2*y* = 300,

The solution table is

| 70 | 80 | 75 |

| 10 | −10 | 0 |

The graphical representation is as follows.