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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

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were



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

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