Five years hence,the age of Jacob will be three times that of his son, 5 years ago,Jacob age was seven times that of his son. What are their present ages?related to ch.pair of linear equations in two variable.?

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Answer

Let present age of jacob be x
and present age of his son be y

5 year letter

x + 5 = 3 (y + 5)
x + 5 = 3y + 15
x - 3y = 10 ...(1)

x - 5 = 7( y - 5 )
x - 5 = 7y - 35
x - 7y = -35 +5
x - 7y = -35 ...(2)

by equation 1st x = 10 + 3y
putting value of x in equation 2nd _x - 7y = -30

10 + 3y - 7y = -30
4y = -30 -10
-4y = -40
4y = 40
y = 40/4 = 10
y = 10

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

jacobs present age (x) = 40 years
and his sons present age will be (y) = 10 years

Answer

Introduction:
In this problem, we will use a pair of linear equations in two variables to find the present ages of Jacob and his son.

Step 1: Assign Variables:
We can assign variables to represent the present ages of Jacob and his son. Let's use 'J' for Jacob's age and 'S' for his son's age.

Step 2: Write Equations:
From the given information, we can write two equations in terms of J and S.

Five years hence, the age of Jacob will be three times that of his son:
J + 5 = 3(S + 5)

Five years ago, Jacob's age was seven times that of his son:
J - 5 = 7(S - 5)

Step 3: Solve the System:
To solve this system of equations, we can use either substitution or elimination method.

Using substitution:
From the first equation, we can solve for J in terms of S:
J + 5 = 3S + 15
J = 3S + 10

Substituting this expression for J in the second equation, we get:
3S + 10 - 5 = 7(S - 5)
3S + 5 = 7S - 35
4S = 40
S = 10

Substituting S = 10 in the first equation, we get:
J + 5 = 3(10 + 5)
J + 5 = 45
J = 40

Therefore, Jacob is currently 40 years old and his son is currently 10 years old.

Using elimination:
Multiplying the first equation by 7, we get:
7J + 35 = 21S + 105

Subtracting the second equation from this, we get:
7J + 35 - J + 5 = 21S + 105 - 7S + 35
6J + 40 = 14S + 140
3J + 20 = 7S + 70
3J = 7S + 50

Multiplying the second equation by 3, we get:
3J - 15 = 21S - 15

Adding this to the previous equation, we get:
6J + 40 + 3J - 15 = 28S + 55
9J + 25 = 28S + 55
9J = 28S + 30

Substituting this expression for J in the first equation, we get:
7(28S + 30) + 35 = 21S + 105
196S + 245 = 21S + 105
175S = -140
S = -0.8

This solution does not make sense, as the age of a person cannot be negative. Therefore, we reject this solution and conclude that the correct solution is J = 40 and S = 10.

Conclusion:
Using a pair of linear equations in two variables, we have found that Jacob is currently 40 years old and his son is currently 10 years old.

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