Question

Four years ago Marina was three years old as her daughter .Six years from now the mother will be twice as old as her daughter.Find the number
It's from Simultaneous linear equation

Answer 1

Correct Question

Four years ago Marina was three times old as her daughter .Six years from now the mother will be twice as old as her daughter. To find the age of mother and daughter.

Answer:

$\boxed{\boxed{\mathsf{Agr\: of\: mother = 34yrs \: And \: age \: of \: Daughter = 14yrs}}}$

Step-by-Step Explanation

√ Given

Four years ago Marina was three years old as her daughter .Six years from now the mother will be twice as old as her daughter.

We need to find the age of daughter and mother.

√ Solution

• The age of daughter be = X
• The age of daughter 4 years ago = x - 4
• The age of daughter 4 years ago = x - 4Age of daughter after 6 years = x + 6

Now According to Question Let

• The age of mother be = y
• The age of mother 4 years ago = y - 4 = 3(x - 4)
• The age of mother after 6 years = y + 6 = 2(x +6)

Therefore we have,

Equation 1 )

$\mathsf{\longrightarrow \: y - 4 = 3(x - 4)}$

$\mathsf{\longrightarrow \: y - 4 = 3x - 12}$

$\mathsf{\longrightarrow \: y = 3x - 8}$

Equation 2 )

$\mathsf{\longrightarrow \: y + 6 = 2(x + 6)}$

$\mathsf{\longrightarrow \: y + 6 = 2x + 12}$

$\mathsf{\longrightarrow \: y = 2x + 12 - 6}$

$\mathsf{\longrightarrow \: y = 2x + 6}$

Now putting value of y from EQ (1) in EQ (2) we have,

$\mathsf{\longrightarrow \: 3x - 8 = 2x + 6}$

$\mathsf{\longrightarrow \: 3x = 2x + 14}$

$\mathsf{\longrightarrow \: 3x - 2x = 14}$

$\mathsf{\longrightarrow \: x = 14}$

Now putting value of X = 14 in EQ(2) we have,

$\mathsf{\longrightarrow \: y = 2(14) + 6}$

$\mathsf{\longrightarrow \: y = 28 + 6}$

$\mathsf{\longrightarrow \: y = 34}$

Therefore we have required answer =

+ Age of daughter = x = 14yrs

+ Age of mother = y = 34yrs

Answer 2

Correct Question :

Four years ago Marina was three times old as her daughter. Six years from now the mother will be twice as old as her daughter. Find the present age from it's Simultaneous linear equation.

AnswEr :

Let the Present Age of Marina be n and Present Age of her daughter be m.

• According to the Question Now :

⋆ Four years ago Marina was three times old as her daughter.

⇝ Marina = 3 Times of her Daughter

⇝ ( n - 4 ) = 3 × ( m - 4 )

⇝ n - 4 = 3m - 12

⇝ 12 - 4 = 3m - n

⇝ 3m - n = 8 — eq. ( I )

⋆ Six years from now the mother will be twice as old as her daughter.

⇝ Marina = Twice of her Daughter

⇝ ( n + 6 ) = 2 × ( m + 6 )

⇝ n + 6 = 2m + 12

⇝ 6 - 12 = 2m - n

⇝ 2m - n = - 6 — eq. ( II )

_________________________________

• Subtracting eq. ( II ) from eq. ( I ) :

⇒ 3m - n = 8

⇒ 2m - n = - 6

- + +

________________

⇒ m = 14 Yrs. — [ Daughter's Present Age ]

• Putting the Value of m in ( I )

⇒ 3m - n = 8

⇒ 3 × 14 - n = 8

⇒ 42 - 8 = n

⇒ n = 34 Yrs. — [ Marina's Present Age ]

∴ therefore, Present Age of Marina is 34 Years and her daughter is 14 Years.