Question

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Answer 1

Answer:

f₁ = 28, f₂ = 32, f₃ = 24.

Step-by-step explanation:

Continuation to attachment:

Given Equations are:

⇒ f₁ + f₂ + f₃ = 84   ---- (i)

⇒ 3f₁ + 5f₂ + 7f₃ = 412   ---- (ii)

⇒ 3f₂ = 4f₃

      f₃ = (3f₂)/4   ---- (iii)

On solving (1) * 3 & (ii), we get

3f₁ + 3f₂ + 3f₃ = 252

3f₁ + 5f₂ + 7f₃ = 412

--------------------------

       -2f₂ - 4f₃ = -160

        2f₂ + 4f₃ = 160.

          f₂ + 2f₃ = 80.   ---- (iv)

Substitute (iii) in (iv), we get

=> f₂ + 2(3f₂)/4 = 80

=> 5f₂ = 160

=> f₂ = 32

Now,

f₂ + 2f₃ = 80

32 + 2f₃ = 80

2f₃ = 48

f₃ = 24

Substitute f₂ and f₃ in (i), we get

=> f₁ + 32 + 24 = 84

=> f₁ + 56 = 84

=> f₁ = 28.

Therefore, the values are:

f₁ = 28

f₂ = 32

f₃ = 24.

Hope it helps!