A library

A library has 12,500 fiction books and 19,000 non fiction books. Currently 2/5 of the fiction books are checked out. Currently 2/5 of the non fiction books are checked out. Of the books checked out, only 1/10 are due back this week. How many books are due this week?

Correct answer:

n =  760

Step-by-step explanation:

$$\begin{gathered} f=12500 \\ v=19000 \\ c={\displaystyle \frac{2}{5}}\cdot c+{\displaystyle \frac{2}{5}}\cdot v={\displaystyle \frac{2}{5}}\cdot 7600+{\displaystyle \frac{2}{5}}\cdot 19000=7600 \\ n={\displaystyle \frac{1}{10}}\cdot c={\displaystyle \frac{1}{10}}\cdot 7600=760 \end{gathered}$$

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