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
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.