For this case we have left over [tex]\frac {3} {4}[/tex]of cake, if each of the guests is taken home[tex]\frac {1} {6}[/tex]of those [tex]\frac {3} {4}[/tex] of leftover cake we have :
[tex]\frac {3} {4} * \frac {1} {6} = \frac {3 * 1} {4 * 6} = \frac {3} {24} = \frac {1} {8}[/tex]
Thus, we have each guest take home[tex]\frac {1} {8}[/tex] of the original cake.
Answer:
Each guest takes home [tex]\frac {1} {8}[/tex] of the original cake.
