The number of students in each section of a school is 24. After admitting new students, three new sections were started. Now, the total number of sections is 16 and there are 21 students in each section. The number of new students admitted is

### Concept & Strategy To find the number of newly admitted students, calculate the difference between the total number of students currently in the school and the original total number of students. $$New\ Students = Current\ Total\ Students - Original\ Total\ Students$$ ### Step-by-Step Solution * **Given:** * Original students per section = 24 * Current total sections = 16 * Current students per section = 21 * New sections added = 3 * **Calculation:** 1. Determine the original number of sections: $Original\ Sections = 16 - 3 = 13$ 2. Calculate the original total number of students: $13\ sections \times 24\ students/section = 312\ students$ 3. Calculate the current total number of students: $16\ sections \times 21\ students/section = 336\ students$ 4. Find the number of new students admitted by taking the difference: $336 - 312 = 24\ students$ ### Exam Strategy & Shortcut You can calculate this using a net change approach to minimize large multiplications. The current 16 sections have 21 students each. The original 13 sections lost 3 students each (dropping from 24 to 21). Total students lost from old sections = $13 \times 3 = 39$. The 3 new sections have 21 students each. Total students in new sections = $3 \times 21 = 63$. The net increase (new students) is the difference: $63 - 39 = 24$. ### Common Pitfall A common mistake is multiplying the 3 new sections by the old section size (24), yielding 72, or multiplying 3 by the new size (21) yielding 63, and assuming that is the answer. This ignores the fact that the original sections were rebalanced. ### Final Answer **Therefore, the correct answer is 24.**