Time Machine backup on machine switch

I have a time machine backup from my old powerbook and when I upgraded to the macbook I used the time machine at the welcome screen. After the machine restored and I ran the first backup on the new machine it backed up my entire drive again. Now my time machine drive it double and a little extra than my actual drive. I tried to see if there are two seperate folders but its all in one. Is there a way to get rid of the old powerbook backups or just format and re backup?