Sarah had a certain amount of money in her bank account. On Monday, she spent $\frac{1}{2}$ of her money plus $10. On Tuesday, she spent $\frac{1}{3}$ of the remaining money plus $10. On Wednesday, she spent $\frac{1}{4}$ of the remaining money plus $10. After these three days, she had $50 left. How much money did Sarah have initially?