Answer:
The whole slices of the cakes of Luke, Kira and Ali are 6, 9 and 12 respectively. So it is possible.
Step-by-step explanation:
It's possible because they cut cakes into different number of slices.
You know that Luke, Kira and Ali each served [tex]\frac{2}{3}[/tex] of their own cake and Luke served 4 slices, Kira served 6 slices and Ali served 8 slices.
Being x the whole slices of cake, and if Luke served [tex]\frac{2}{3}[/tex] of his cake, which are 4 slices, the whole slices of cake of Luke is:
[tex]\frac{2}{3}*x=4 slices[/tex]
Solving:
x= 4 ÷[tex]\frac{2}{3}[/tex]
x= 6
Then, whole slices of Luke's cake is 6.
Performing the same approach for Kira you get:
[tex]\frac{2}{3}*x=6 slices[/tex]
x= 6 ÷[tex]\frac{2}{3}[/tex]
x= 9
Then, whole slices of Kira's cake is 9.
Finally, performing the same approach for Ali you get:
[tex]\frac{2}{3}*x=8 slices[/tex]
x= 8 ÷[tex]\frac{2}{3}[/tex]
x= 12
Then, whole slices of Ali's cake is 12.
The whole slices of the cakes of Luke, Kira and Ali are 6, 9 and 12 respectively. So it is possible.
