Question

a certain medicine is given in an amount proportional to a patients body weight. suppose a patient weighing 150 pounds requires 144 milligrams of medicine. what is the weight of a patient who requires 174.72 milligrams of medicine?
pounds

Explanation:

Step1: Find the proportionality constant

Let the weight be \( w \) (in pounds) and the medicine amount be \( m \) (in milligrams). Since they are proportional, \( m = kw \), where \( k \) is the constant. For \( w = 150 \) and \( m = 144 \), we find \( k=\frac{m}{w}=\frac{144}{150}=0.96 \).

Step2: Calculate the patient's weight

We know \( m = 174.72 \) and \( k = 0.96 \). Using \( m = kw \), we solve for \( w \): \( w=\frac{m}{k}=\frac{174.72}{0.96} \).

Step3: Perform the division

\( \frac{174.72}{0.96}=182 \).

Answer:

182