A baker started with a certain number of cookies. On Monday, he sold $\frac{1}{2}$ of his cookies plus 5. On Tuesday, he sold $\frac{1}{3}$ of the remaining cookies plus 10. On Wednesday, he sold $\frac{1}{4}$ of the remaining cookies plus 15. After these three days, he had 30 cookies left. How many cookies did the baker have initially?