BTDT with both kids. Do I ignore it? Depends why they're whiny. If they're sick, I give them extra TLC. Otherwise I'll say, "Sorry, I don't respond to whining," and then I ignore them. If they don't get the message I'll whine back to them and exaggerate so they realize what it sounds like and how annoying it is.
A good article:
Whining: Why it happens and what to do about it - ParentCenter