Let \( x \) be the number of pages that Taylor read. According to the problem, Arlene read 30 pages, which is 10 pages more than half of what Taylor read. We can express this relationship with the following equation:
\[ 30 = \frac{1}{2}x + 10 \]
To write this in the form \( px + q = r \), we first rearrange the equation:
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Subtract 10 from both sides: \[ 30 - 10 = \frac{1}{2}x \] which simplifies to: \[ 20 = \frac{1}{2}x \]
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Multiply both sides by 2 to eliminate the fraction: \[ 2 \cdot 20 = x \] This leads to: \[ 40 = x \]
Now, we can formally express this problem in the requested form. Rearranging \( 20 = \frac{1}{2}x \) gives:
\[ \frac{1}{2}x - 20 = 0 \]
To fit it into the standard \( px + q = r \) format, we rewrite it as:
\[ \frac{1}{2}x - 20 = 0 \]
or, multiplying through by 2 to clear the fraction,
\[ x - 40 = 0 \]
Thus the equation can be represented as:
\[ x + (-40) = 0 \]
So \( p = 1 \), \( q = -40 \), and \( r = 0 \).
The final equation in the required format is:
\[ x - 40 = 0 \]
Taylor read 40 pages.