Let's denote the number of pages Taylor read as \( x \).
According to the information provided:
- Arlene read 30 pages.
- This is 10 pages more than half of what Taylor read.
We can set up the equation from the given information:
\[ 30 = \frac{1}{2}x + 10 \]
Now, we need to rearrange this into the form \( px + q = r \).
First, isolate the term with \( x \):
- Subtract 10 from both sides:
\[ 30 - 10 = \frac{1}{2}x \]
\[ 20 = \frac{1}{2}x \]
- To eliminate the fraction, multiply both sides by 2:
\[ 2 \cdot 20 = x \]
\[ 40 = x \]
Now to write our final equation in the form \( px + q = r \):
Starting from our adjusted equation before eliminating the fraction:
\[ \frac{1}{2}x - 20 = 0 \]
If we multiply the entire equation by 2 to avoid fractions, we will have:
\[ x - 40 = 0 \]
Thus, in the form \( px + q = r \):
\( 1x + (-40) = 0 \)
In summary, our final equation in the required form is:
\[ 1x - 40 = 0 \]
So, Taylor read 40 pages.
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