You can use the factors of the volumes 24, 27 and 48:
For example:
8 by 3 by 1 is a total volume of 24
or if you know that 4 times 2 is 8:
4 by 2 by 2
and so on
There are no solutions to the given system of equations.
Hope this helps.
12-x(5-4k)=y
12-y=x(5-4k)
12-y/(5-4k)=x