Math, asked by yashsudhirdixit16, 2 months ago

cost of 4 pencils and 3 pens and 2 eraser is rupees 60 the cost of the 2 pencils 4pens and 6 eraser is rupees 90 where is the cost of the 6 pencil to 2pen and 3 eraser is rupees 70 find the cost of each atom by using the matrix​

Answers

Answered by Itzgoldenking
2

Answer:

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step-by-step explanation:

Let the cost of pencils, pens &  erasers per dozen be denoted as Rs. “x”, Rs. “y” & Rs. “z” respectively.

According to the question let’s write the equations first:

4x + 3y + 2z = 60 ….. (i)

2x + 4y + 6z = 90 ….. (ii)

6x + 2y + 3z = 70 …… (iii)

Since we are asked to solve the cost of each item by using matrices, so let’s arrange the equation in matrix form:

 4     3      2           x             60

 2     4      6           y       =    90           i.e., AX = B

 6     2      3           z             70        

R₂ → [R₂ - 1/2R₁] & R₃ → [R₃ - 3/2R₁]

  4       3        2          x              60

  0     5/2      5          y        =    90

  0    -5/2     0           z              70

R₃→ [R₃ + R₂]

  4       3        2          x               60

  0      5/2     5          y    =         90

  0       0       5          z                70

From the above matrix that we got, we can now write,  

5z = 40

⇒ z = 40/5 = 8 …… (iv)

And,

5/2y + 5z = 60

⇒5/2y + (5*8) = 60

⇒ 5/2y = 60 - 40

⇒ y = 20*2/5 = 8 ….. (v)

Now, by substituting the values of y & z from (iv) & (v) in eq. (i), we get

4x + (3*8) + (2*8) = 60

⇒ 4x = 60 – 16 – 24

⇒ x = 20/4 = 5

Thus, the cost of 1 dozen pencil is Rs. 5, 1 dozen pens is Rs. 8 and 1 dozen eraser is Rs. 8.

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