Question

a certain medicine is given in an amount proportional to a patients body weight. suppose a patient weighing 200 pounds requires 250 milligrams of medicine. what is the weight of a patient who requires 220 milligrams of medicine?
pounds

Explanation:

Step1: Define Proportional Relationship

Let \( w \) be weight (pounds) and \( m \) be medicine (milligrams). Since \( w \propto m \), we can write \( w = km \), where \( k \) is the constant of proportionality.

Step2: Find Constant \( k \)

Given \( w = 200 \) when \( m = 250 \), substitute into \( w = km \):
\( 200 = k \times 250 \)
Solve for \( k \): \( k = \frac{200}{250} = \frac{4}{5} \).

Step3: Calculate Weight for 220 mg

Now, use \( w = \frac{4}{5}m \) with \( m = 220 \):
\( w = \frac{4}{5} \times 220 \)
\( w = 4 \times 44 = 176 \).

Answer:

176