Answer:
To determine the balance of iron supplement dose and ordinary food servings needed to meet the patients' nutritional needs, let's assign variables to represent the quantities:
Let:
- x = number of iron supplement doses per day
- y = number of ordinary food servings per day
Based on the information given, we can establish the following equations:
Equation 1: Iron Balance
1.2µg * x + 0.4µg * y = 5.2µg
Equation 2: Potassium Balance
0.3mg * x + 0.1mg * y = 1.3mg
We can solve this system of equations to find the values of x and y that satisfy both equations.
Multiplying Equation 1 by 10 and Equation 2 by 1000 will help us eliminate the decimal points:
Equation 1 (revised): 12µg * x + 4µg * y = 52µg
Equation 2 (revised): 300µg * x + 100µg * y = 1300µg
Now, we can use any method to solve the equations. Let's solve them using the substitution method:
From Equation 1 (revised), we can express x in terms of y:
12µg * x = 52µg - 4µg * y
x = (52µg - 4µg * y) / 12µg
x = (13µg - µg * y) / 3µg
x = 13/3 - y/3
Substituting this value of x into Equation 2 (revised):
300µg * (13/3 - y/3) + 100µg * y = 1300µg
Simplifying and solving for y:
(3900µg - 100µg * y + 100µg * y) / 3 = 1300µg
3900µg / 3 = 1300µg
1300µg = 1300µg
The equation is satisfied for any value of y. This means that there is no unique solution for the system of equations. In other words, any combination of iron supplement doses (x) and ordinary food servings (y) that satisfy the equation 1.2µg * x + 0.4µg * y = 5.2µg will also satisfy the equation 0.3mg * x + 0.1mg * y = 1.3mg.
Therefore, there are multiple ways to achieve the balance of iron and potassium needed to meet the patients' nutritional needs. The specific values of x and y will depend on the preferences of the patients and the dosing recommendations by healthcare professionals.