Library visitors

Sixty percent of library visitors borrow detective stories or science fiction and nothing else, one-fifth only classic literature and one-tenth only non-fiction. Other library visitors only borrow poetry. In September, 168 library visitors borrowed classic literature. How many total library visitors were there in September? How many visitors rented a detective or sci-fi book in September? What percentage of visitors borrow classic literature or non-fiction?

Correct answer:

n =  840
d =  504
p =  30 %

Step-by-step explanation:

$$\begin{gathered} \frac{1}{5}n=168 \\ n=168\cdot 5=840 \end{gathered}$$

$$\begin{gathered} r_1=60\%=\frac{60}{100}=\frac{3}{5}=0.6 \\ d=r_1\cdot n=0.6\cdot 840=504 \end{gathered}$$

$$\begin{gathered} z=\frac{1}{5}\cdot n+\frac{1}{10}\cdot n=\frac{1}{5}\cdot 840+\frac{1}{10}\cdot 840=252 \\ p=100\cdot \frac{z}{n}=100\cdot \frac{252}{840}=\frac{100\cdot 252}{840}=\frac{25200}{840}=30\% \end{gathered}$$

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