She used not to fast during Ramadan when she first reached puberty; should she make them up now that she has grown up?

She has to work out the number of days when she did not fast according to what she thinks is most likely, and fast them with the intention of making them up, until she is certain that she has made up all the days that she owes. As well as that, she should feed one poor person for each day, so as to be on the safe side and to avoid an area of scholarly difference of opinion, if she is able to feed others. 

For more information on feeding the poor, please see the answer to question no. 26865. 

If she is fasting on Mondays and Thursdays, then she should intend that to make up what she owes, so that she will complete the days that she owes. 

Shaykh Saalih al-Fawzaan was asked: If a girl reaches the age of puberty before the month of Ramadan begins, but she does not fast that year in which she reached puberty because she is not aware that fasting is obligatory for her, what does she have to do? Is the ruling in this case the same as the ruling as one who breaks the fast deliberately with no excuse? 

He replied: She has to repent to Allah, may He be glorified and exalted, and make up the same number of fasts as the days that she missed, and she also has to feed one poor person for each day, if the next Ramadan came and she had not fasted those days. End quote. 

Al-Muntaqa fi Fatawa al-Fawzan, 81/11 

And Allah knows best.