Question

The sum of the ages of two sisters, Mary and Jane, is 24 years. Four years ago three times Mary’s age was 3 years more than twice Jane’s age

Answer 1

Given :

• The sum of the ages of two sisters, Mary and Jane, is 24 years.

• Four years ago three times Mary’s age was 3 years more than twice Jane’s age

To find :

• Present age of Mary and Jane?

Solution :

⠀⠀❏⠀Let Present age of Mary be x years

⠀⠀❏⠀And, Present age of Jane be y years.

• Sum of their ages is 24 years.

➵ x + y = 24

➵ x = 24 - y⠀⠀⠀⠀⠀⠀❲ eq (1) ❳

★ According to the Question:

• Four years ago three times Mary’s age was 3 years more than twice Jane’s age.

Their ages before 4 years,

• Age of Mary = (x - 4) years
• Age of Jane = (y - 4) years

Therefore,

➵ 3(x - 4) = 3 + 2(y - 4)

➵ 3x - 12 = 3 + 2y - 8

➵ 3x - 12 = 2y - 5⠀⠀⠀⠀⠀⠀❲ eq (2) ❳

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Putting eq (1) in eq (2),

➵ 3(24 - y) - 12 = 2y - 5

➵ 72 - 3y - 12 = 2y - 5

➵ - 3y + 60 = 2y - 5

➵ - 3y - 2y = - 5 - 60

➵ - 5y = - 65

➵ y = -65/-5

➵ y = 13

Now, Putting value of y in eq (1),

x = 24 - 13

x = 11

Therefore,

• Present age of Mary, x = 11 years
• Present age of Jane, y = 13 years

∴ Hence, Present age of Mary and Jane is 11 years and 13 years respectively.

Answer 2

Step-by-step explanation:

Given :

• The sum of the ages of two sisters, Mary and Jane, is 24 years.

• Four years ago three times Mary’s age was 3 years more than twice Jane’s age.

To Find :

1. Present age of Mary = ?
2. Present age of Jane = ?

Solution :

$\dag\:\:\textsf{Let Mary's age be \textbf{x years.}}$

• $\dag\:\:\textsf{Then, Jane's age will be \textbf{24 - x years.}}$

$\large\bigstar \: \underline{\textsf{Four years ago :}}$

$\dag\:\:\textsf{Mary was \textbf{x - 4 years.}}$

$\dag\:\:\textsf{and Jane was 24 - x - 4 = \textbf{20 - x years.}}$

$\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies \sf 3(x - 4) = 2(20 - x) + 3$

$:\implies \sf 3x - 12= 40 - 2x + 3$

$:\implies \sf 3x - 12= 43 - 2x$

$:\implies \sf 3x + 2x= 43 + 12$

$:\implies \sf 5x= 55$

$:\implies \sf x= \dfrac{55}{5}$

$:\implies \underline{ \boxed{\sf x= 11 \: years} }\qquad \Bigg\lgroup \textsf{\textbf{Age of Mary}}\Bigg\rgroup$

$\underline{\boldsymbol{Present\: age \:of\: Mary\:and\:Jane :}}$

• $\: \: \textsf{Present age of Mary = x = \textbf{11 years}}.$

• $\: \: \textsf{Present age of Jane = 24 - x = 24 - 11 = \textbf{13 years}}.$