Are you referring to your onboard account or things you specifically need to pay with cash?
We took maybe $100 on our 3 night cruise and probably the same amount for our 5 night. The only things we used cash for was souvenirs in Nassau. Everything else is charged to your shipboard account which varies depending on what you do/purchase. When just DH and I sailed without our children on a 3 night our bill was $260. That included adult dining in Palo, mixology, bikes on Castaway Cay, regular gratuities, room service tips, specialty coffees and alcoholic drinks. We had onboard credit from our TA and we applied a gift card to our account immediately after boarding so we actually had very little to pay at the end of the cruise.
When all 4 of us took a 5 night last year the total bill was less than $100 BUT we prepaid gratuities ($240). We bought a couple of photos, the boys each got a sword in the gift shop, we bought souvenir cups, tips for room service and I think that was it. We used cash in Nassau for souvenirs.
What you spend really depends on what you are planning to do.