Question

a certain medicine is given in an amount proportional to a patient’s body weight. suppose a patient weighing 159 pounds requires 202 milligrams of medicine. what is the amount of medicine required by a patient weighing 129 pounds?
milligrams

Explanation:

Step1: Find proportionality constant

Let \(m\) = medicine (mg), \(w\) = weight (lb). Since \(m \propto w\), \(m = kw\). Substitute \(m=212\), \(w=159\):
\(k = \frac{212}{159} = \frac{4}{3}\)

Step2: Calculate medicine for 129 lb

Use \(m = \frac{4}{3}w\), substitute \(w=129\):
\(m = \frac{4}{3} \times 129 = 4 \times 43 = 172\)

Answer:

172 milligrams