Question

In addition to low iron levels, some of your patients have had high potassium levels while

taking NT71C. While reviewing the data during rounds, you and your colleagues estimate
that the patients need 5.2µg of iron and 1.3mg of potassium each day. The iron
supplements you've purchased contain 1.2µg of iron and 0.3mg of potassium per dose,
while the patient's daily meals contain 0.4µg of iron and 0.1 mg of potassium per serving.
What balance of iron supplement dose and ordinary food servings should you use to
meet the patients' nutritional needs?

Answer 1

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.