Answer
78.37 cups are required for $LD_{50}$ of caffeine
Work Step by Step
Size of cup = 12 fl oz
Since there is 100 mg of caffeine / 6 fl oz of coffee, amount of caffeine in a cup = 2 x 100 mg = 200 mg
$LD_{50}$ of caffeine = 192 mg/kg
Weight of person = 180 lb
1 kg = 2.205 lb
180 lb x 1 kg / 2.205 lb = 81.63 kg
$LD_{50}$ of caffeine for 81.63 kg = 192 mg/kg x 81.63 kg
= 15673.47 mg
Amount of fluid required = 15673.47 mg / 100 mg / fl oz
= 156.73 fl oz
Cups required = 156.73 fl oz / 2 = 78.37 cups
