A dietician works in a hospital and prepares meals under the guidance of a physician. Suppose that for a particular​ patient, a physician prescribes a meal to h

Question

A dietician works in a hospital and prepares meals under the guidance of a physician. Suppose that for a particular patient, a physician prescribes a meal to have 950 calories, 65 g of protein, and 340 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

                      Calories        protein                  vitamin C

 

 steak               300             20g                         0

 

 Potato              100              5g                       20mg

 

 Brussel Sprout     50                 5g                    100mg

 

 TOTALS            950              65g                    340 mg

 

 

             

 

300S + 100P + 50B = 950

 

20S + 5P + 5B = 65

 

          20P + 100B = 340

 

 

----------------------------------------

 

 

 

6S + 2P + B = 19  <--- 1st equation: divides everything by 50

4S + P + B = 13 <--- 2nd equation : divides everything by 5

      P + 5b = 17 <---- 3rd equation: divides everything by 20

 

 

Elimination method:eliminates P as follows.....

 

Subtracts EQUATION #2 MINUS Equation #3:

4S  - 4B = -4 

S - B = -1 

S = B-1 <--- please label this equation ALPHA

 

THEN subtracts EQUATION #1 MINUS 2 * Equation 3:

6S - 9B = -15

2S - 3B = -5 <--- please label this equation BETA

 

Substitutes equation ALPHA INTO equation BETA

 

2(B-1) - 3B = -5

2B - 2 - 3B = -5

-B - 2 = -5

B+2=5

B = 3

By equation ALPHA, S = B-1 = 3-1 = 2

 

Finally P + 5b = 17

         P + 5(3) = 17

         P + 15 = 17

         P = 2

 

 

                                                  calories              protein             vitamin C

2 servings of steak                       600                    40 g                        0

3 servings of brussel sprouts         150                    15 g                       300 mg

2 servings of potatoe                     200                   10 g                        40 mg

-----------------------------------------------------------------------------------------------

TOTALS                                   950                       65g                   340 mg