Let's define the variables for the problem:
- Let \( t \) be the number of pages Taylor read.
- According to the problem, Arlene read 30 pages, which is stated to be 10 more than half the pages Taylor read.
We can express this relationship in an equation. According to the description:
\[ 30 = \frac{1}{2}t + 10 \]
Now, we want to rearrange this into the form \( Px + q = R \).
First, subtract 10 from both sides:
\[ 30 - 10 = \frac{1}{2}t \] \[ 20 = \frac{1}{2}t \]
Next, multiply both sides by 2 to eliminate the fraction:
\[ 40 = t \]
Now we have \( t = 40 \).
To express the equation in the requested form \( Px + q = R \):
- Rearranging \( 30 = \frac{1}{2}t + 10 \) gives us: \[ -\frac{1}{2}t + 30 - 10 = 0 \] which simplifies to: \[ -\frac{1}{2}t + 20 = 0 \]
In the form \( Px + q = R \), we can express this as:
\[ -\frac{1}{2}t + 20 = 0 \]
Where:
- \( P = -\frac{1}{2} \)
- \( q = 20 \)
- \( R = 0 \)
So, the final equation is:
\[ -\frac{1}{2}t + 20 = 0 \]
Thus, Taylor read 40 pages.
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