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The cost of 4kg potato 3kg wheat and 2 kg rice is 150 the cost of 1 kg potato 2 kg wheat 3 kg rice is 125 the cost of 6 kg potato 2 kg wheat and 3 kg rice is 175 find the cost of each item per kg by using Cramer's rule ?
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The cost of 4kg potato 3kg wheat and 2 kg rice is 150 the cost of 1 kg...
Using Cramer's Rule to Find Cost per kg of Items
Given Information:
- Let the cost of 1 kg of potato be x, 1 kg of wheat be y, and 1 kg of rice be z.
- From the given information, we have the following equations:
1. 4x + 3y + 2z = 150
2. x + 2y + 3z = 125
3. 6x + 2y + 3z = 175
Setting up the Determinants:
- We will set up determinants for x, y, and z using Cramer's Rule.
- The determinant D will be the determinant of the coefficients of x, y, and z.
- The determinant Dx will be the determinant of the coefficients of x, replacing the x-column with constants.
- Similarly, the determinant Dy and Dz will be calculated.
Calculating Determinants:
- D = |4 3 2|
|1 2 3|
|6 2 3|
= 4(6*3 - 2*2) - 3(1*3 - 2*6) + 2(1*2 - 2*6)
= 48 - 9 + 10
= 49
- Dx = |150 3 2|
|125 2 3|
|175 2 3|
= 150(6*3 - 2*2) - 3(125*3 - 2*175) + 2(125*2 - 6*175)
= 900 - 225 + 50
= 725
- Dy = |4 150 2|
|1 125 3|
|6 175 3|
= 4(125*3 - 2*175) - 150(1*3 - 2*6) + 2(1*175 - 125*6)
= 1150 - 225 + 50
= 975
- Dz = |4 3 150|
|1 2 125|
|6 2 175|
= 4(2*175 - 125*3) - 3(1*175 - 125*6) + 150(1*2 - 2*6)
= 950 - 375 + 150
= 725
Calculating Cost per kg:
- x = Dx / D = 725 / 49 = 14.80
- y = Dy / D = 975 / 49 = 19.90
- z = Dz / D = 725 / 49 = 14.80
Therefore, the cost per kg of potato is $14.80, wheat is $19.90, and rice is $14.80.
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The cost of 4kg potato 3kg wheat and 2 kg rice is 150 the cost of 1 kg potato 2 kg wheat 3 kg rice is 125 the cost of 6 kg potato 2 kg wheat and 3 kg rice is 175 find the cost of each item per kg by using Cramer's rule ?
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The cost of 4kg potato 3kg wheat and 2 kg rice is 150 the cost of 1 kg potato 2 kg wheat 3 kg rice is 125 the cost of 6 kg potato 2 kg wheat and 3 kg rice is 175 find the cost of each item per kg by using Cramer's rule ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The cost of 4kg potato 3kg wheat and 2 kg rice is 150 the cost of 1 kg potato 2 kg wheat 3 kg rice is 125 the cost of 6 kg potato 2 kg wheat and 3 kg rice is 175 find the cost of each item per kg by using Cramer's rule ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cost of 4kg potato 3kg wheat and 2 kg rice is 150 the cost of 1 kg potato 2 kg wheat 3 kg rice is 125 the cost of 6 kg potato 2 kg wheat and 3 kg rice is 175 find the cost of each item per kg by using Cramer's rule ?.
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