In 2010, a library contained a total of 11,500 books in two categories –…
2024
In 2010, a library contained a total of 11,500 books in two categories – fiction and non-fiction. In 2015, the library contained a total of 12,760 books in these two categories. During this period, there was a 10% increase in the fiction category, while there was a 12% increase in the non-fiction category. How many fiction books were in the library in 2015?
Answer: A. 6600 — This is a mixture-style percentage problem: when two sub-groups of a total grow at different rates and only the new combined total is known, set up one linear…
- A.
6600
- B.
6160
- C.
6000
- D.
5500
Attempted by 17 students.
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Correct answer: A
This is a mixture-style percentage problem: when two sub-groups of a total grow at different rates and only the new combined total is known, set up one linear equation for the original totals and a second for the increased totals, then solve the pair for the unknowns.
Let F = fiction books and N = non-fiction books in 2010, so F + N = 11,500.
After the given increases, the 2015 total is 1.10F + 1.12N = 12,760 (a 10% rise on fiction, a 12% rise on non-fiction).
From the first equation, N = 11,500 − F. Substitute into the second: 1.10F + 1.12(11,500 − F) = 12,760.
Expand and simplify: 1.10F + 12,880 − 1.12F = 12,760, so −0.02F = −120, giving F = 6,000.
Fiction books in 2015 = 1.10 × 6,000 = 6,600.
Cross-check: non-fiction books in 2010 = 11,500 − 6,000 = 5,500, so non-fiction books in 2015 = 1.12 × 5,500 = 6,160. Total for 2015 = 6,600 + 6,160 = 12,760, which matches the given total — confirming the result.
So the library had 6,600 fiction books in 2015.
