# NCERT Solutions, CBSE Sample paper, Latest Syllabus, NCERT Books, Last Year Question Papers and Many More ...

## 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.

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.

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

Question 1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you we