Let \( x \) represent the number of pages Taylor read. According to the problem, half of the pages Taylor read is represented as \( \frac{x}{2} \).
Arlene read 30 pages, which is 10 pages more than half of the pages Taylor read. This relationship can be expressed in the following equation:
\[ \frac{x}{2} + 10 = 30 \]
To put this equation in the form \( px + q = r \), we can rearrange it. First, subtract 10 from both sides:
\[ \frac{x}{2} = 20 \]
Now, multiply both sides by 2 to eliminate the fraction:
\[ x = 40 \]
To represent the original equation in the form \( px + q = r \), we can multiply through by 2 to clear the fraction:
\[ x + 20 = 60 \]
Thus, the final equation in the required form is:
\[ 1x + 20 = 60 \]
This shows \( p = 1 \), \( q = 20 \), and \( r = 60 \).
So, Taylor read 40 pages.