The blinded condition says:
The creature cannot see. It takes a –2 penalty to Armor Class, loses its Dexterity bonus to AC (if any), and takes a –4 penalty on most Strength– and Dexterity-based skill checks and on opposed Perception skill checks. All checks and activities that rely on vision (such as reading and Perception checks based on sight) automatically fail. All opponents are considered to have total concealment (50% miss chance) against the blinded character. Blind creatures must make a DC 10 Acrobatics skill check to move faster than half speed. Creatures that fail this check fall prone. Characters who remain blinded for a long time grow accustomed to these drawbacks and can overcome some of them.
The Stealth skill says:
Your Stealth check is opposed by the Perception check of anyone who might notice you. Creatures that fail to beat your Stealth check are not aware of you and treat you as if you had total concealment. You can move up to half your normal speed and use Stealth at no penalty. When moving at a speed greater than half but less than your normal speed, you take a –5 penalty. It’s impossible to use Stealth while attacking, running, or charging.
Again, emphasis mine
When blind and using stealth, is half your normal speed still half-speed for the purposes of avoiding the DC 10 Acrobatics check? Or does using stealth make it so that your "normal speed" is halved, and you must move at a quarter-speed to avoid the DC 10 Acrobatics check?
To clarify the question: if using stealth while blind, can you move at half-speed without any penalty to the stealth check and still avoid making DC 10 Acrobatics checks every move action to avoid falling?