help me please

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 550 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 Brussel 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

Hi JP,

1 (3 Oz) steak serving contains: 300 calories 20g protein   0mg vitamin C
1  Baked potato serving contains: 100 calories   5g protein 20mg vitamin C
1  Brussels sprout serving contains:  50 calories   5g protein 100 mg vitamin C

Prescription calls for 550 calories, 40 grams of protein and 320mg of vitamin C
x= servings of steak, y = servings of baked potato, z = serving of Brussels sprout

 

Write the equation for calories totals
300x + 100y + 50z = 550
6x + 2y + z =11 eq1
Write equation for total protein
20x + 5y + 5z = 40
4x +y +z = 8 eq2
Write the equation for total vitamin C
0x + 20y + 100z = 320
y + 5z = 16
y = 16 - 5z eq3
Plug eq3 into eq2
4x+16-5z +z =8
4x + 8 - 4z = 0
x + 2 - z =0
z = x + 2 eq4
Now plug eq3 into eq1
6x + 2(16 – 5z) + z = 11
6x + 32 -10z +z = 11
6x + 21 – 9z = 0 plug z from eq4 here
6x + 21 -9(x + 2) =0
6x +21 -9x -18 =0
-3x +3 = 0
x = 1, plug this into equation eq4
z = 3, plug this into equation eq3
y = 1

1 serving of Steak 300 calories 10g protein 0 mg vitamin C
3 servings of Brussels sprout 150 calories 15g protein 300mg vitamin C
1 serving of Baked potato 100 calories 5g protein 20mg vitamin C