SOLUTION: A dietitian wants a patient to have meal with 66 grams of protein, 94.5 grams of carbohydrates, and 910 milligrams of calcium. The meal is composed of chicken, corn, milk. Each se

Algebra ->  Matrices-and-determiminant -> SOLUTION: A dietitian wants a patient to have meal with 66 grams of protein, 94.5 grams of carbohydrates, and 910 milligrams of calcium. The meal is composed of chicken, corn, milk. Each se      Log On


   

Question 343462: A dietitian wants a patient to have meal with 66 grams of protein, 94.5 grams of carbohydrates, and 910 milligrams of calcium. The meal is composed of chicken, corn, milk. Each serving of chicken has 30 grams of protein, 35 grams of carbs, and 200 milligrams of calcium. Each serving of corn has 3 grams of protein, 16 grams of carbs, and 10 milligrams of calcium. Each serving of milk has 9 grams of protein, 13 grams of carbs, and 300 milligrams of calcium. How many servings of each need to be given to the patient?
I got the problems set up like this:
chicken=x
corn=y
milk=z
30x+3y+9z=66
35x+16y+13z=94.5
200x+10y+300z=910
I am pretty sure I need to do matrices , but don't know how to break it down? Can you please help me?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You don't necessarily need to solve using matrix methods but it is fastest.
You could also use substitution or elimination.
[A]=%28matrix%283%2C3%2C30%2C3%2C9%2C35%2C16%2C13%2C200%2C10%2C300%29%29
[x]=%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29
[b]=%28matrix%283%2C1%2C66%2C94.5%2C910%29%29
[A][x]=[b]
[x]=[A]inv[b]
.
.
.
Find the inverse of [A].
det[A]=90750
.
.
.
[A]inv=
.
.
.
[x]=%28matrix%283%2C1%2C1.5%2C1%2C2%29%29