Free notebooks were distributed equally among the children of a class. The…
2025
Free notebooks were distributed equally among the children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed?
- A.
256
- B.
432
- C.
512
- D.
640
Attempted by 5 students.
Show answer & explanation
Correct answer: C
Concept: This is an indirect (inverse) proportion set-up: the total number of notebooks distributed is a fixed quantity, so it can be written as (number of children) times (notebooks per child) in either scenario, and the two expressions for that same total must be equal.
Let the number of children be n. Each child gets n/8 notebooks, so the total notebooks distributed = n × (n/8) = n²/8.
If the number of children were halved to n/2, each child would get 16 notebooks, so the total notebooks distributed in that scenario = (n/2) × 16 = 8n.
Since both expressions describe the very same total, set them equal: n²/8 = 8n.
Divide both sides by n (n ≠ 0): n/8 = 8, which gives n = 64.
Substitute n = 64 into the total: total notebooks = 8n = 8 × 64 = 512.
Cross-check: with n = 64 children, each child originally gets 64/8 = 8 notebooks, so the total is 64 × 8 = 512. Halving the children gives 32 children; 512 ÷ 32 = 16 notebooks each, matching the given condition exactly. Both scenarios confirm the total is 512.