Answer :
Answer:
1/6 of the original cake was left
Step-by-step explanation:
Let
x ----> complete cake
we know that
1) John ate 1/6 of the cake
so
The remaining cake is equal to
[tex]x-\frac{1}{6}x=\frac{5}{6}x[/tex]
2) Susan ate 1/5 of what was left
so
[tex](\frac{1}{5})\frac{5}{6}x=\frac{1}{6}x[/tex]
The remaining cake is equal to
[tex]\frac{5}{6}x-\frac{1}{6}x=\frac{4}{6}x=\frac{2}{3}x[/tex]
3) Chan ate 1/4 of what was left after that
so
[tex](\frac{1}{4})\frac{2}{3}x=\frac{2}{12}x=\frac{1}{6}x[/tex]
The remaining cake is equal to
[tex]\frac{2}{3}x-\frac{1}{6}x=\frac{3}{6}x=\frac{1}{2}x[/tex]
4) Cindy ate 1/3 of what was left after that
so
[tex](\frac{1}{3})\frac{1}{2}x=\frac{1}{6}x[/tex]
The remaining cake is equal to
[tex]\frac{1}{2}x-\frac{1}{6}x=\frac{2}{6}x=\frac{1}{3}x[/tex]
5) Luigi ate 1/2 of what was left after that
so
[tex](\frac{1}{2})\frac{1}{3}x=\frac{1}{6}x[/tex]
The remaining cake is equal to
[tex]\frac{1}{3}x-\frac{1}{6}x=\frac{1}{6}x[/tex]
therefore
1/6 of the original cake was left