Bash script question

I have the following command in a bash script:

list_of_files =`find *.tgz -mtime +10'

but instead of using 10 i want to pass a variable. I have tried the following:

list_of_files=`find *.tgz -mtime +"$MAX_DAYS"`

list_of_files=`find *.tgz -mtime +$MAX_DAYS`


Any ideas?

Thanks