Magic Keyboard is Devouring Batteries - any solutions?

Three weeks ago my keyboard started gobbling at least 2 pair of fully charged batteries per day (often 3 pair per day). I have no idea how to fix it and am unsure if the problem is with the keyboard or computer. The batteries are not the issue - I purchased 24 new ones... I've always used energizer rechargeables in both the keyboard and mouse without any problem.

I'm using the 1st generation magic keyboard and magic mouse on a 2010 iMac OS X Yosemite 10.10.5 There are no other bluetooth devices connected.

I'd like to purchase a new keyboard as a last resort considering I just acquired $36 worth of batteries...