1. **State the problem:** Milan puts $\frac{1}{4}$ of her laundering money in savings and uses $\frac{2}{3}$ of the remaining money to pay back her sister. After these transactions, she has 15 left. We need to find how much money she had at first. 2. **Define the variable:** Let the total amount of money Milan had at first be $x$. 3. **Calculate the amount after savings:** She puts $\frac{1}{4}$ of $x$ in savings, so the remaining money is: $$x - \frac{1}{4}x = \frac{3}{4}x$$ 4. **Calculate the amount used to pay back sister:** She uses $\frac{2}{3}$ of the remaining $\frac{3}{4}x$ to pay back her sister: $$\frac{2}{3} \times \frac{3}{4}x = \frac{2}{4}x = \frac{1}{2}x$$ 5. **Calculate the amount left after paying sister:** The money left after paying sister is the remaining money minus what she paid: $$\frac{3}{4}x - \frac{1}{2}x = \frac{3}{4}x - \frac{2}{4}x = \frac{1}{4}x$$ 6. **Set up the equation:** We know this leftover amount is 15, so: $$\frac{1}{4}x = 15$$ 7. **Solve for $x$:** Multiply both sides by 4: $$\cancel{\frac{1}{4}}x \times 4 = 15 \times 4$$ $$x = 60$$ **Final answer:** Milan had 60 at first.