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.​

Answer 1

Given :-

• 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.

To Find :-

• Solve the following problem Algebraically and graphically.

Solution :-

Let consider, Aftab's daughter's present age be " x " years.

And Aftab's present age be " y " years$.$

Now,

7 years ago,

The daughter's (past) age = ( x - 7 ) years.... (1)

The Father's (past) age = ( y - 7 ) years.... (2)

3 years after

The daughter's age (future) = ( x + 3 ) years.... (3)

The Father's age (future) = ( y + 3 ) years.... (4)

According to the question :-

In 1st case

Father's (past) age = 7 × Daughter's Age { From (1) and (2) }

➹ y - 7 = 7(x - 7 )

➹ y - 7 = 7x - 49

➹ 7x - y - 49 + 7 = 0

➹ 7x - y - 42 = 0

In 2nd case

Father's (future) age = 3 × Daughter's (future) age { from (3) and (4) }

➹ y + 3 = 3(x + 3)

➹ y + 3 = 3x + 9

➹ 3x - y + 9 - 3 = 0

➹ 3x - y + 6 = 0

Therefore,

Algebraically the two situations can be represented as follows :-

➹ 3x - y + 6 = 0 ..... (5)

➹ 7x - y - 42 = 0.....(6)

Lets make Table for equation (1)

• If x = 6 then y = 24
• If x = 12 then y = 42

Then, Table for equation (2)

• If x = 12 then y = 42
• If x = 18 then y = 84

Note :- For graphically representation, refer to the attachment.

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Answer 2

■ 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.

■ Given :-

➬ 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

■ What I have to do :-

➭ represent this situation algebraically and graphically.

■ SolutiOn :-

Let the present age of Aftab be x .

And present age of his daughter be y .

According to first situation ,

After seven years ago,

➧ Age of Aftab = (x - 7 )

➧ Age of his daughter = ( y - 7 )

Now,

( x - 7 ) = 7( y - 7 )

➨ x - 7 = 7y - 49

➨ x - 7y = -49 + 7

➨ x - 7y = -42 ----------------(1)

According to second situation ,

After three years ago,

➧ Age of Aftab = (x + 3 )

➧ Age of his daughter = ( y + 3 )

Now,

( x + 3 ) = 3( y + 3 )

➨ x + 3 = 3y + 9

➨ x + 3y = 9 ----------------(2)

Therefore,

The algebraic represention is

x - 7y = -42

➱ x - 3y = 6

➱ For , x - 7y = -2

Therefore, x = -2 + 7y

Imp :- The suitable table is in the attachment.

For x - 3y = 6

➱ x = 6 + 3y

Imp :- The suitable table is in the attachment.

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Note :-

See the attachment for suitable table .

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