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Form the pair of linear equations for the following problems and find their solution by substitution method. (vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are

Q3.    Form the pair of linear equations for the following problems and find their solution by substitution method.

                (vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

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Let x be the age of Jacob and y be the age of Jacob's son,

Now, According to the question 

x+5=3(y+5)

\Rightarrow x+5=3y+15

\Rightarrow x-3y=10..........(1)

Also,

x-5=7(y-5)

\Rightarrow x-5=7y-35

\Rightarrow x-7y=-30.........(2)

Now,

From (1) we have,

x=10+3y...........(3)

Substituting this value of x in (2) 

10+3y-7y=-30

\Rightarrow -4y=-30-10

\Rightarrow 4y=40

\Rightarrow y=10

Substituting this value of y in (3),

x=10+3y=10+3(10)=10+30=40

Hence, Present age of Jacob is 40 years and the present age of Jacob's son is 10 years.

 

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