Respuesta :
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
Food A is 5 ounces, Food B is 1 ounce, and Food C is 4 ounces and this can be determined by forming the linear equation in three variables.
Given :
- The nutritional content per ounce of three foods is presented in the given table.
- A meal consisting of the three foods allows exactly 1800 calories, 75 grams of protein, and 5650 milligrams of vitamin C.
Let the total amount of Food A be 'A', total amount of Food B be 'B', and the total amount of Food C be 'C'.
The linear equation that represents total calories in each food is:
100A + 500B + 200C = 1800
[tex]\rm A =\dfrac{ 1800 - 500B-200C}{100}[/tex]
[tex]\rm A =18 - 5B-2C[/tex] --- (1)
The linear equation that represents total protein in each food is:
5A + 6B + 11C = 75 ---- (2)
The linear equation that represents total Vitamin C in each food is:
400A + 2050B + 400C = 5650 --- (3)
Now, substitute the value of 'A' in equation (2).
[tex]\rm 5(18-5B-2C)+6B+11C=75[/tex]
Simplify the above equation.
90 - 25B - 10C + 6B + 11C = 75
C - 19B = -15
C = 19B - 15 ---- (4)
Now, substitute the value of 'C' in equation (1).
A = 18 - 5B - 2(19B - 15)
A = 18 - 5B - 38B + 30
A = 48 - 43B --- (5)
Now, substitute the value of A and C obtains in equations (4) and (5) in equation (3).
A = 5 ounces
B = 1 ounce
C = 4 ounces
For more information, refer to the link given below:
https://brainly.com/question/2263981
