Q. 14.0( 513 Votes )
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 :
Given: Seven years ago, Aftab was seven times as old as his daughter and after 3 years Aftab will be 3 times as old as his daughter.
To Represent the situations algebraically and graphically we need to find the linear equations for these situations.
Let present age of Aftab = x
Let present age of his daughter = y
Then, seven years ago the age of Aftab and his daughter must have been seven less than their present ages,
Age of Aftab seven years ago = x – 7
Age of Daughter seven years ago = y – 7
According to the question,
Seven years ago, Aftab was seven times as old as his daughter, Sox - 7 = 7(y - 7)
⇒ x - 7 = 7y - 49
⇒ x = 7y - 42
Putting y = 5, 6 and 7 in equation (¡),
we get,For y = 5,
x = 7 × 5 – 42
= 35 – 42
= -7
For x =6,
x = 7 × 6 – 42
= 42 – 42
= 0
For y = 7,
x = 7 × 7 – 42
= 49 – 42
= 7
Thus we got 3 points to plot on graph for this equation.
Three years from now,
Age of Aftab = x+3
Age of Daughter = y+3
According to the question,
⇒ x + 3 = 3(y + 3)
⇒ x + 3 = 3y + 9
⇒ x = 3y + 6
Putting x = 0, 3 and 6
Thus we got 3 points to plot on graph for this equation.
Algebraic representation
x - 7y = -42 (i)
x - 3y = 6 (ii)
Graphical representation:
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