1. **State the problem:** Yasmin, Kian, and Maggie have scores in the ratio 3 : 5 : 12, and the mean of their scores is 180. We need to find Yasmin's score. 2. **Understand the ratio and mean:** The ratio 3 : 5 : 12 means if Yasmin's score is $3x$, Kian's is $5x$, and Maggie's is $12x$ for some $x$. 3. **Use the mean formula:** The mean of their scores is given by $$\text{Mean} = \frac{\text{Sum of scores}}{\text{Number of people}}$$ Here, the mean is 180 and the number of people is 3. 4. **Set up the equation:** $$180 = \frac{3x + 5x + 12x}{3}$$ Simplify the numerator: $$180 = \frac{20x}{3}$$ 5. **Solve for $x$:** Multiply both sides by 3: $$180 \times 3 = 20x$$ $$540 = 20x$$ Divide both sides by 20: $$x = \frac{540}{20} = 27$$ 6. **Find Yasmin's score:** Yasmin's score is $3x$: $$3 \times 27 = 81$$ **Final answer:** Yasmin's score is 81.