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

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

age of Aftab is represented by       x

age of daughter is represented by y

Then Seven years ago,

age of Aftab              = x -7

 age of daughter       = y-7

given that I was seven times as old as you were  so we get

x  - 7    = 7 ( y – 7 )

x – 7    = 7 y – 49

x- 7 y   = - 49 + 7       

x – 7 y = - 42                          …(1)

x         = 7 y  –  42   

plug y = 5,6 and 7 we get

x          =  7 * 5  - 42   =  35 -  42       = - 7

x          = 7 * 6 -  42    =  42 – 42       =0

x          =  7 * 7  – 42 = 49 – 42         = 7

X	-7	0	7
y	5	6	7

three years from now ,

Age of Aftab              = x +3

 Age of daughter      = y+3

Given that I shall be three times as old as you will be so we get

x + 3    = 3 (y + 3)

x + 3    = 3 y + 9

x -3 y =  9- 3

x -3 y  = 6                              …(2)

x         =  3 y + 6                   

plug  y = -2,-1and 0 we get

x          =  3 * - 2  + 6 = -6+6 =0

x          =  3 * - 1  + 6 = -3+ 6             = 3

x          =  3 * 0 +  6 =  0 +  6             = 6

X	0	3	6
y	-2	-1	0

Algebraic representation

From equation (1)  and (2)

x – 7 y    = –  42                     …(1)

x - 3 y   = 6                           …(2)

Graphical representation