I mention that every adult is screened, that applicant must make 3x the rent, and whether or not pets are accepted.

I started my adult working life in sales at a big box retailer.

It is typical for all adults residing in the property to be required to sign the lease.

Should all adults who will be living in the property always be on the lease agreement?

I have a NJ rental (good 5 bedroom rental house, but not so good neighborhood and therefore not so good tenants). 3 adults, 4 kids and pets. 10 months prior to the end of the lease (All 3 adults signed one lease.

There's one adult 3 kids..

Consider the most important qualifiers and focus on those.Let them know you will be running a credit/criminal background check on every adult.

My exception to the credit score rule would be if the tenant had NO score at all, which likely indicates they are an immigrant, just starting out in adult life, or a huge Dave Ramsey fan.

This helps spot additional adults living there, unauthorized pets, and property damage.

Find new tenants, do not sublet or give control to the remaining party (who is not on the lease, every adult should be on the lease).