matricies please help

Question

A dietician works in a hospital and prepares meals under guidance of a physician. suppose for a particular patient, a physician prescribes a meal to have 750 calories, 40 g of protein, and 320 mg of vitamin C. The dietician decides to prepare the meal using steak (each 3- oz serving contains 300 Cal, 20 g of protein, and no vitamin C), baked potatoes (one baked potato contains 100 Cal, 5 g of protein and 20 mg of vitamin C), and Brussels sprouts (one 156-g serving contains 50 Cal,5 g of protein, and 100 mg of vitamin C). How many servings of each food are required to satisfy the physician’s requirements?

Answer 1

S = number of 3-oz servings of steak, each having 300 cal, 20 g of protein, and 0 mg of vitamin C

P= number of baked potatoes, each potato having 100 cal, 5g of protein, and 20 mg of vitamin C

B = number of 156 g servings of Brussels sprouts, each having 50 cal, 5g of protein, and 100 mg of vitamin C 

 

Write an equation for each of the requirements.  Each equation will be a weighted combination of S, P, and B, yielding the required total.

 

Calories:

 

(300 cal/serving)S + (100 cal/serving)P + (50 cal/serving)B = 750 cal 

 

Proteins:

 

(20 g/serving)S + (5g/serving)P + (5g/serving)B = 40 g

 

Vitamin C:

 

(0 mg/serving)S + (20 mg/serving)P + (100 mg/serving)B = 320 mg

 

You now have a system of 3 linear equations in 3 unknowns S, P, and B.  Solve for S, P, and B:

 

300S + 100P + 50B = 750

20S  + 5P + 5B = 40

(0)S + 20P + 100B = 320

 

Rounded to 2 decimal places, I get

 

S = -0.33 servings of of steak (3-oz each serving)

P = 7.67 servings of potatoes (1 potato per serving) 

B = 1.67 servings of Brussels sprouts (156 g per serving)

 

There is a problem, because the number of steak servings comes out negative.  Could you double-check the numbers in the problem statement?