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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.

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Solution

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

[tex]\begin{gathered} A\propto W \\ \\ \Rightarrow A=kW \\ \\ \Rightarrow k=\frac{A}{W} \end{gathered}[/tex]

when W = 150, A = 3g

[tex]\begin{gathered} \Rightarrow k=\frac{3}{150}=\frac{1}{50} \\ \\ \Rightarrow A=\frac{1}{50}W \end{gathered}[/tex]

When W = 225

[tex]\Rightarrow A=\frac{225}{50}=4.5[/tex]

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

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