The advice above about extending with Airport Express is spot on, but in your situation I would recommend a slightly different approach that might get tricky.
Since your base station is quite old (6 yrs) I would opt for a new AirPort Extreme or Time Capsule to use as a replacement base station. To this I would add an Airport Express and relocate your old AirPort Extreme to your Garage addition.
The Airport Express I would locate midway between your new and old bases.
With only fifty feet between you might be able to get by without the addition of an Airport Express, but you may run into signal strength problems without it.
Alternately, you could run an Ethernet cable to the new addition and attach an Airport Express that way also.
Hope this helps.
EDIT: For what it's worth my house is a 2100 sqft tri-level and I originall ran it with a TimeCapsule base station with an AirPort Extreme to extend the network. That worked OK with occasional signal loss (especially in the upstairs bedroom). Currently I am running two Time Capsules, an AirPort Extreme, and an Airport Express. Probably overkill, but seems to work well.