1. **State the problem:** Sarah sampled 20 students with an average study time of 15 hours per week. Susan sampled 30 students with an average study time of 12 hours per week. We need to find the combined average study time for all 50 students. 2. **Formula used:** The combined average is a weighted average calculated by $$\text{Combined average} = \frac{(n_1 \times \bar{x}_1) + (n_2 \times \bar{x}_2)}{n_1 + n_2}$$ where $n_1$ and $n_2$ are the sample sizes, and $\bar{x}_1$ and $\bar{x}_2$ are the sample means. 3. **Apply the values:** $$\text{Combined average} = \frac{(20 \times 15) + (30 \times 12)}{20 + 30}$$ 4. **Calculate numerator:** $$20 \times 15 = 300$$ $$30 \times 12 = 360$$ 5. **Sum numerator:** $$300 + 360 = 660$$ 6. **Sum denominator:** $$20 + 30 = 50$$ 7. **Calculate combined average:** $$\frac{660}{50}$$ 8. **Simplify fraction:** $$\frac{\cancel{660}}{\cancel{50}} = \frac{66}{5} = 13.2$$ 9. **Final answer:** The combined average study time is **13.2 hours per week**.