Plenty of good options below.
Another way to think of this is to think from a population perspective and not split it upfront but start with overall usage for those that do not have access to personal machines
So calculate # of household and % of population with access to laundry at home - like you have already done
Then population that does not have indiviual access at home (live in apartments without laundry in unit so use building laundry etc.) Make assumptions on number of laundry machines per 100 people and calculate laundry machines needed here
Then look at special population needs - e.g., students, hospitals, laundromats, hotels. and make individual assumptions - e.g., students you can use the same number as what you calculate for population without individual machines, for hospitals and hotels you might need different assumptions and maybe even the same one.
Hope this helps