A researcher is analyzing a large dataset. On the first day, she processes $\frac{1}{4}$ of the data plus 15 records. On the second day, she processes $\frac{1}{3}$ of the remaining data plus 20 records. On the third day, she processes $\frac{1}{2}$ of the remaining data plus 25 records. After these three days, there were 35 records left to process, which she completed on the fourth day. How many records were in the original dataset?