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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

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

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Solution

Let the present age of father be \(x\) years and the age of daughter be \(y\) years
Seven years ago father's age\(=(x-7)\)yr
Seven years ago daughter's age\(=(y-7)\)yr
According to the problem\(,(x-7)=7(y-7)\)
or \(x-7y=-42\cdots\cdots(i)\)
After 3 yr father's age\(=(x+3)\)yr
After 3 yr daughter's age\(=(y+3)\)yr
According to the condition given in the questions
\( x+3=3( y+3) \)
or  \(x-3y=6 \cdots \cdots (ii)\)
Hence, algebraically the situation is represented by equations
\(x-7y=-42\)
\(x-3y=6\) where \(x\) is the present age of father and \(y\) is the present age of his daughter.
To find the equivalent geometric representation\(,\) we find some points on the line representing each equation\(.\) These solutions are given below in the table\(.\)
From \(Eq.(i),x-7y=-42\)

From \(Eq.(ii),x-3y=6\)


Hence, situation is represented graphically.
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