Question

In 2010, a library contained a total of 11500 books in two categories -fiction and nonfiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?

• A. 6000
• B. 6160
• C. 5500
• D. 6600

Answer 1

The Correct Option is D

Let the number of fiction books in 2010 be \( x \), and the number of non-fiction books be \( y \).

Step 1: Use the given data

• Total number of books in 2010: \( x + y = 11{,}500 \)     (1)
• In 2015:
  • Fiction books increase by 10% → \( 1.1x \)
  • Non-fiction books increase by 20% → \( 1.2y \)
• Total books in 2015: \( 1.1x + 1.2y = 12{,}760 \)     (2)

Step 2: Solve the system of equations

From equation (1):

\[ x + y = 11{,}500 \Rightarrow y = 11{,}500 - x \]

Substitute into equation (2):

\[ 1.1x + 1.2(11{,}500 - x) = 12{,}760 \] \[ 1.1x + 13{,}800 - 1.2x = 12{,}760 \] \[ -0.1x + 13{,}800 = 12{,}760 \] \[ -0.1x = -1{,}040 \Rightarrow x = \frac{-1{,}040}{-0.1} = 6{,}000 \]

Step 3: Calculate fiction books in 2015

\[ \text{Fiction books in 2015} = 1.1x = 1.1 \times 6{,}000 = 6{,}600 \]

Answer:

There were 6,600 fiction books in the library in 2015.