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iTunes can do that...

Set iTunes preferences -> Advanced -> Importing -> Import Using to MP3 Encoder at your desired bitrate under Setting, then (after pressing OK) hold down the option key and click the Advanced menu in iTunes and choose the Convert to MP3... (do not choose it id it says Convert Selection to MP3), find your aiff files (you can choose the folder(s) they're in) and the songs are converted to MP3 and added to iTunes (no need to import the aiffs first)...
 
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