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.
Answer:
Let the present age of Aftab be x.
And, present age of his daughter = y
Seven years ago,
Age of Aftab = x − 7
Age of his daughter = y − 7
According to the question,
(x – 7) = 7 (y – 7)
x – 7 = 7y – 49
x – 7y = –42 (1)
Three years hence,
Age of Aftab = x + 3
Age of his daughter = y + 3
According to the question,
(x + 3) = 3 (y + 3)
x + 3 = 3y + 9
x – 3y = 6 (2)
Therefore, the algebraic representation is
x – 7y = –42
x – 3y = 6
For x – 7y = –42
x = –42 + 7y
The solution table is
For x – 3y = 6,
x = 6 + 3y
The solution table is
The graphical representation is as follows.
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