To find: The quantity of each ingredient bought.
The weight of each ingredient added is 1 lb.
Given information:
Given, to fill three 1-lb bags with a trail mix. Almonds cost $2.25/lb, peanuts cost $1.30/lb, and raisins cost $0.90/lb. The mix contains twice as much nuts as raisins by weight. Exactly $4.45 is spent on the ingredients.
Calculation:
Let the weight of almonds be x lb, peanuts be y lb and raisins be z lb.
Three 1-lb bags total weight is 3 lb i.e.,
The cost equation is given by
Given that the weight of nuts is twice as much as raisins. So,
Hence the system of equations is:
The matrix equation is given by:
Multiplying both sides by the inverse of the matrix on the left gives the required solution.
The determinant of the matrix is given by:
Since the determinant is not 0, the inverse exists.
The inverse of a 3X3 matrix
The cofactor matrix is given by:
The adjoint matrix is the transpose of cofactor matrix.
Hence the adjoint matrix is given by:
Hence the inverse matrix of the given matrix is given by:
Multiplying both sides of the equation by the inverse:
Conclusion:
The weight of each ingredient added is 1 lb.
Chapter 12 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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