Let the total number of books Mr. Peters bought be \( x \).
According to the information given:
- 75% of all the books he bought were paperbacks.
- The number of paperback books he bought is 15.
We can set up the equation based on the information provided:
\[ 0.75x = 15 \]
To find \( x \), we need to solve for it:
\[ x = \frac{15}{0.75} \]
Calculating the right side:
\[ x = 20 \]
Therefore, Mr. Peters bought a total of 20 books.