1. **State the problem:** We have a language school where 39 7/12 % learn Chinese, 31 1/4 % learn German, and the remaining 210 learn Japanese. We need to find: (a)(i) Total number of students in the school. (a)(ii) Number of students learning Chinese. (b) Number of students who passed the German Proficiency Examination. 2. **Convert percentages to decimals:** - Chinese: 39 7/12 % = 39 + 7/12 = 39 + 0.5833 = 39.5833% = 0.395833 - German: 31 1/4 % = 31 + 1/4 = 31.25% = 0.3125 - Remaining (Japanese): 100% - (39.5833% + 31.25%) = 100% - 70.8333% = 29.1667% = 0.291667 3. **Find total number of students:** Given Japanese students = 210 = 29.1667% of total. Let total students be $T$. $$0.291667 \times T = 210$$ Solve for $T$: $$T = \frac{210}{0.291667} = 720$$ 4. **Find number of students learning Chinese:** $$\text{Chinese students} = 0.395833 \times 720 = 285$$ 5. **Calculate students who sat for German exam:** German students = $$0.3125 \times 720 = 225$$ 80% of German students sat for the exam: $$0.8 \times 225 = 180$$ 6. **Calculate number who passed:** 30% failed, so 70% passed: $$0.7 \times 180 = 126$$ **Final answers:** - (a)(i) Total students = 720 - (a)(ii) Chinese students = 285 - (b) Students who passed German exam = 126