Question

Find the total cost of 2kg salt 3/2 of rice and 5kg wheat

Answer 1

Sugar = Rs 40, Wheat = Rs 18 and Rice = Rs 25

Step-by-step explanation:

Let the cost of 1 kg of sugar be Rs x

Let the cost of 1 kg of wheat be Rs y

Let the cost of 1 kg of rice be Rs z

∴Cost of 5 kg sugar, 5 kg wheat, 2 kg rice = Rs 340

 Cost of 2 kg sugar, 5 kg wheat, 4 kg rice = Rs 270

 Cost of 4 kg sugar, 3 kg wheat, 2 kg rice = Rs 264

Required system of linear equations:

5x + 5y + 2z = 340

2x + 5y + 4z = 270

4x + 3y + 2z = 264  

Let A = , X = and B =

∴ AX = B

Pre multiplying by A⁻¹,

X =  A⁻¹B  ..............1

For matrix A,

|A| = 5(10-12) -5(4-16) +2(6-20)

or |A| = 22

Thus, A is invertible

Finding cofactors of matrix A

C₁₁ = -2, C₁₂ = 12, C₁₃ = -14

C₂₁ = -4, C₂₂ = 2, C₂₃ = 5

C₃₁ = 10, C₃₂ = -16, C₃₃ = 15

∴Cofactor matrix of A =

∴ adj A =

Therefore,  A⁻¹ = 1/ |A| ( adj A)

or A⁻¹ = 1/22

Substituting in equation 1,

 = 1/22

or   = 1/22

or = 1/22

or =

Thus, x=40, y=18, z=25

Cost of 1 kg of sugar is Rs 40

Cost of 1 kg of wheat is Rs 18

Cost of 1 kg of rice is Rs 25.