Question

The nutritional content per ounce of three foods is presented in the table below. If a meal consisting of the three foods allows exactly
1800 calories, 75 grams of protein, and 5650 milligrams of vitamin C, how many ounces of each kind of food should be used?
Food A
Food B
Food C
Calories
100
500
200
Protein
(in grams)
5
6
11
Vitamin C
(in milligrams)
400
2050
400
Food A:
OZ
Food B:
OZ
Food C:
OZ

Answer 1

Answer:

A = 5 ounces

B = 1 ounces

C = 4 ounces

Step-by-step explanation:

The 3 foods contain exactly 1800 calories but food A is 100 calories, food B is 500 calories and food C is 200 calories. Thus;

100A + 500B + 200C = 1800 - - - (eq 1)

The 3 meals allows exactly 75 grams of protein while A is 5 grams, B is 6 grams, C is 11 grams.

Thus;

5A + 6B + 11C = 75 - - - (eq 2)

The 3 meals allows exactly 5650 milligrams of vitamin C while A is 400 mg, B is 2050 mg and food C is 400 mg. Thus;

400A + 2050B + 400C = 5650 - -(eq 3)

Solving the 3 equations simultaneously online, we have;

A = 5 ounces

B = 1 ounces

C = 4 ounces