The Library Book Budget
A school library has 480 books to distribute across three reading levels: Beginner, Intermediate and Advanced. The librarian wants the number of Beginner books to be twice the number of Advanced books, and the number of Intermediate books to be 40 more than the number of Advanced books. After distributing the books, she notices that 1 in every 8 Beginner books is damaged and must be replaced. Replacement books cost $6 each, and the library has a budget of $250 for replacements. She must decide whether the budget is enough, and if not, how many damaged books she cannot replace.
1. How many books are assigned to each reading level?
Read the worked answer
Let the number of Advanced books be a.
- Beginner = 2a
- Intermediate = a + 40
- Total: 2a + (a + 40) + a = 480
So 4a + 40 = 480, giving 4a = 440 and a = 110.
- Advanced = 110
- Beginner = 220
- Intermediate = 150
Check: 220 + 150 + 110 = 480. ✓
2. Is the $250 replacement budget enough? Show your reasoning.
Read the worked answer
Damaged Beginner books = 1/8 of 220 = 27.5.
Since a book is either damaged or not, the count must be a whole number. The problem says '1 in every 8', which describes a rate, not an exact count. The most reasonable reading is that about 27 or 28 books are damaged.
- At 27 damaged: 27 × $6 = $162
- At 28 damaged: 28 × $6 = $168
Both totals are well under $250, so the budget is enough. The leftover is $250 − $168 = $82 (or $88 if 27 books are damaged).
The key judgement here is recognising that '1 in 8' is a rate and rounding sensibly rather than reporting 27.5 books.