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 algebrically and graphically.


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Answer 1

Answer:

→ Hey User,

→ Given 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 algebrically and graphically.

→ To find :-  Represent this situation algebrically and graphically.

→ Solution :-

→ Let the actual age of Aftab be = $x$   years.

→ Let the actual age of daughter be = $y$  years.

→ According to 1 st condition :-

→  7 years ago Aftab age = ( x - 7 )

→ 7 years ago Daughter age = ( y - 7 )

→ so , ( x - 7 )  =  7  ( y - 7 )

→          x-7      = 7y - 49

→        x-7y      =  - 49  + 7

→   [     x-7y      =   -42 ]      ----------------- ( equation 1 )

→ According to second condition :-

→ The Age of Aftab after 3 years = ( x + 3 )

→ The Age of Daughter after 3 years = ( y + 3 )

→ so ,  ( x + 3 ) = 3  ( y + 3 )

→          x + 3   =  3y  + 9

→          x - 3y = 9 - 3

→    [ x - 3y = 6 ]    -------------------------     ( Equation 2 )

→ [ 1 st equation = x - 7y = -42 ]

→ [ 2nd equation = x- 3y = 6   ]  

→ Is the answer.  

→ Now , x - 7y = -42

→ Let  x = 0

→ 0 - 7y = -42

→ -7y = $\frac{42}{7}$   ( after canceling thevalue remains 6 )

→ [ y = 6 ]

→ Now , Graph ( x ,y)

→                     p ( 0 , 6 )

→  Let  ( y = 0 )

→ x - 7 ( 0 )  = -42

→ x -0  = -42

→[  x = -42 ]  

→ Again from second Equation :-

→ x-3y = 6      equation second

→ Let  ( x = 0 )

→ 0 - 3y = 6

→ -3y = 6

→[  y = $\frac{6}{-3}$  ] = [ y = -2 ]   {  ( 0,2)  let 0 be point r }

→ Again ,

→ Let y = 0

→ x - 3y = 6

→ x -3 ( 0 )=6

→ x - 0 = 6

→  [ x = 6 ]             5 ( 6 ,0 )    

hope it helps ,  

thank you

   

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Answer 2

Given  :  seven years ago, Aftab was seven times as old as his daughter .

three years from now, Aftab shall be three times as old as his daughter will be

To Find : Current ages

Solution:

Current ages of aftab = x

Current age of daughter = y

Seven year ago aftab age = x - 7

7 years ago daughter age = y - 7

x - 7 = 7 (y - 7)

=> x = 7y  - 42

3 year after aftab age = x + 3

3 year after daughter age = y + 3

x + 3 = 3(y + 3)

=> x = 3y  + 6

x = 7y  - 42

x = 3y  + 6

=> 7y - 42 = 3y + 6

=> 4y = 48

=> y = 12

=> x = 3(12)+ 6 = 42

Aftab age =   42 years

Daughter  age =  12  

from graph also intersection point is ( 42 , 12)

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