It may be cheaper to have a new solid core door installed. A new solid core door is heavier and can be ordered in a pre-hung configuration. Of course, if you’re renting then your out of luck and should use the foam idea. By the way, foam isn’t a bad idea, but the solid core door coupled with foam would be ideal. New doors are less than $200, and a good handyman can hang it for around $100. Good luck!