Question

a certain medicine is given in an amount proportional to a patients body weight. suppose a patient weighing 159 pounds requires 212 milligrams of medicine. what is the amount of medicine required by a patient weighing 129 pounds? milligrams

Explanation:

Step1: Set up proportionality equation

Let $m$ = medicine amount (mg), $w$ = weight (lbs). Since $m \propto w$, $m = kw$, where $k$ is the constant of proportionality.

Step2: Solve for $k$ using given values

Substitute $w=159$, $m=212$:
$212 = k \times 159$
$k = \frac{212}{159} = \frac{4}{3}$

Step3: Calculate medicine for 129 lbs

Substitute $w=129$, $k=\frac{4}{3}$ into $m=kw$:
$m = \frac{4}{3} \times 129$

Answer:

172 milligrams