Let's denote the number of pages Taylor read as \( x \).
According to the problem, Arlene read 30 pages, which is 10 pages more than half of the pages Taylor read. We can translate this statement into the following equation:
\[ 30 = \frac{1}{2}x + 10 \]
To rearrange this equation into the form \( px + q = r \), we will first isolate \( \frac{1}{2}x \) by subtracting 10 from both sides:
\[ 30 - 10 = \frac{1}{2}x \]
This simplifies to:
\[ 20 = \frac{1}{2}x \]
Next, we can multiply both sides by 2 to eliminate the fraction:
\[ 40 = x \]
Now, we can rearrange it into the required format \( px + q = r \):
\[ x - 40 = 0 \]
Thus, the final equation in the required form is:
\[ 1x - 40 = 0 \]
This shows that Taylor read 40 pages.