Answer :
Solution.
Given
A lethal dose of caffeine for a 135 lb person is 9184 mg of caffeine.
[tex]\begin{gathered} Let\text{ L represent the weight \lparen in lb\rparen of a person} \\ Let\text{ w represent the mg of caffeine dose} \\ The\text{ proportion is a direct one because an increase in lb will bring about increase in mg and vice versa\rparen} \\ L\text{ }\alpha\text{ w} \\ L\text{ =kw \lparen where k = constant\rparen} \end{gathered}[/tex][tex]\begin{gathered} k=\frac{L}{w}=\frac{135}{9184} \\ Thus, \\ L=\frac{135}{9,184}w \\ The\text{ required proportion is } \\ L=\frac{135}{9,184}w \end{gathered}[/tex]For a 150 lb person, L = 150
[tex]\begin{gathered} L=\frac{135}{9,184}w \\ 150\text{ = }\frac{135}{9184}w \\ w=\frac{150\text{ x 9184}}{135} \\ w=10204.44\text{ mg} \end{gathered}[/tex]The lethal dose of caffeine for a 150 lb person is 10204.44 mg
