Question

13. The amount of medicine that a physician prescribes for a patientvaries directly as the weight of the patient. A physician prescribes 3 gof medicine for a 150-lb person. How many grams should be prescribedfor a 225-lb person? Set up the equation and solve.

Answer 1

Given that the Amount of Medicine (A) varies directly with the weight of the patient (W)

`\begin{gathered} A\propto W \\ \\ \Rightarrow A=kW \\ \\ \Rightarrow k=(A)/(W) \end{gathered}`

when W = 150, A = 3g

`\begin{gathered} \Rightarrow k=(3)/(150)=(1)/(50) \\ \\ \Rightarrow A=(1)/(50)W \end{gathered}`

When W = 225

`\Rightarrow A=(225)/(50)=4.5`

Therefore, 4.5 grams should be prescribed for a 225 - lb person.