1997 Toyota Corolla Battery Charges. Master Brake main pr

Engine Performance problem
1997 Toyota Corolla 4 cyl Automatic

Couldn't get the mileage. Anyways, the car was bought 2 months ago from a friend.A friend of mine owns the car and it's been a problem. He always ends up recharging the vehicle. Now he stated he called a mechanic and observed what happened he stated "it's the master break" because of the fact that from pedal if according to my friend "when he steps on the brake pedal it's all the way touching the car carpet. So the problem is per the mechanic "it's in the engine (from me personally, he was pointing directly to the assembly next to the fan belt and on top is the alternator). And my friend stated the cost of the "part" is about $70-$90. The maine PROBLEM of the car, dying out. My question is the alternator is alright but am guessing the battery needs to be changed, right? Alright am just a friend trying to help a crazy friend of mine from getting ripped from a mechanic from our home town.