Question

Age of Remya and double of Sofi added together gives 28. Three-fourth of Remya's age added to one-fourth of Sofi's age gives 11. Find the age of Remya and the age of Sofi. Explain using X and Y​

Answer 1

GivEn:

• Age of Remya and double of Sofi added together gives 28.
• ¾ of Remya's age added to ¼ of Sofi's age gives 11.

To find:

• Present age of Remya and Sofi?

Solution:

☯ Let Present age of Remya and Sofi be x and y respectively.

★ According to the Question:

• Sum of age of Remya and double age of Sofi is 28.

➯ 2y + x = 28

➯ x = 28 - 2y⠀⠀⠀⠀⠀⠀⠀ ❬ eq (❶) ❭

• Sum of ages of ¾ of Remya's age and ¼ of Sofi's age is 11.

➯ 3/4 x + 1/4 y = 11

➯ (3x + y)/4 = 11

➯ 3x + y = 11 × 4

➯ 3x + y = 44⠀⠀⠀⠀⠀⠀⠀ ❬ eq (❷) ❭

⠀━━━━━━━━━━━━━━━━━━━━━

Now, Substituting eq (1) in eq (2),

➯ 3(28 - 2y) + y = 44

➯ 84 - 6y + y = 44

➯ 84 - 5y = 44

➯ - 5y = 44 - 84

➯ - 5y = - 40

➯ y = 40/5

➯ y = 8

Now, Substitute value of "y" in eq (1),

➯ x = 28 - 2(8)

➯ x = 28 - 16

➯ x = 12

Hence,

• Present age of Remya, x = 12 years
• Present age of Sofi, y = 8 years

Answer 2

Answer:

Given :-

• Age of Remya and double of Sofi added together gives 28. Three-fourth of Remya 's age added to one-fourth of Sofi's age gives 11 .

To Find :-

• What is the age of Remya and Sofi.

Solution :-

» Let, the age of Remya be x years

» And, the age of Sofi will be y years

➣ According to the question,

➛ First, age of Remya and double the age of Sofi added together gets 28,

⇒ x + 2y = 28

⇒ x = 28 - 2y ..... equation no ❶

➛ Now, three-fourth of Remya age added to one-fourth of Sofi's age gets 11,

⇒ $\dfrac{3}{4}$x + $\dfrac{1}{4}$y = 11

➛ Multiplying both sides with 4, we get,

⇒ 3x + y = 44 .... equation no ❷

➛ Putting the equation no (1) in the equation no (2), we get

⇒ 3(28 - 2y) + y = 44

⇒ 84 - 6y + y = 44

⇒ - 5y = 44 - 84

⇒ - 5y = - 40

⇒ y = $\sf\dfrac{\cancel{- 40}}{\cancel{- 5}}$

➠ y = 8 years

➛ By putting y = 8 in the equation no (1) we get,

⇒ x = 28 - 2(8)

⇒ x = 28 - 16

➠ x = 12 years

$\therefore$ The age of Remya is 12 years and the age of Sofi is 8 years .