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 550 ​calories, 35 g of​ protein, and 140 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

The food servings required to satisfy the physician's requirements: one 3-oz serving of steak, one 156-g serving of Brussels sprouts and two baked potatoes.

Explanation:

The patient needs a meal having 550 calories, 35 g of protein and 140 mg of vitamin C.

Total calorie required = 550 .............................................................equation (1)

calories in one serving of steak = 300 ............................................ equation (2)

calories in one baked potato = 100 ............................................ equation (3)

calories in one serving of Brussels sprouts = 50 .......................... equation(4)

Total calories in one serving of each food = equation (2) + (3) + (4)

= 300 + 100 +50 = 450 ....equation(5)

The balance calorie required = equation (1) - (5)

= 550 - 450 = 100 ............................ equation (6)

Total protein needed = 35 g ............................................................ equation (7)

Protein in one serving of steak = 20 g................................................. equation (8)

Protein in one baked potato = 5 g ................................................ equation (9)

Protein in one serving of Brussels sprouts = 5 g .......................... equation(10)

Total protein in one serving of each food = equation (8) + (9) + (10)

= 20 + 5 + 5 = 30 g .... equation(11)

The balance protein required = equation (7) - (11)

= 35 - 30 = 5 g ..................................... equation (12)

Total Vitamin C needed = 140 mg ................................................ equation (13)

Vitamin C in one serving of steak = 0 mg ....................................... equation (14)

Vitamin C in one baked potato = 20 mg .................................... equation (15)

Vitamin C in one serving of Brussels sprouts = 100 mg ............... equation(16)

Total Vitamin C in one serving of each food = equation (14) + (15) + (16)

= 0 + 20 + 100 = 120 mg ... equation(17)

The balance Vitamin C required = equation (13) - (17)

= 140 - 120 = 20 mg ..................... equation (18)

From equations (6), (12) and (18), the required calories, protein and vitamin C after one serving of each food items is 100 calories, 5 g of protein and 20 mg of vitamin C, which is the equivalent of one baked potato.

Hence, one 3-oz serving of steak, one 156-g serving of Brussels sprouts and two baked potatoes meets the physician's prescribed meal requirements.