The Slums are still less expensive than living in a district. Living in the outcasts quarter costs 50 sparks per decade for rent, plus at least 20 sparks for food (canned). If you spend an extra 30 sparks per week on food in the Slums, you're breaking even, but once you reach a higher level of health (and the Hip's 3 spark meals can get you to B+), you can maintain it by eating out every fourth day (assuming we remove the -1 nightly on the day when you eat out, you get +2 for that day and -1 for each subsequent day, so after the third night you're back to where you were before the meal).
You save on bathing if you live in the outcasts district, but you don't need to bathe regularly in the Slums, that's a luxury, and it is included in slave training costs/rewards when you take the slave to the beach.