Let's break down the information given in the problem.
We know that:
- Arlene read 30 pages.
- This amount is 10 more than half the pages that Taylor read.
Let's define the variable:
- Let \( T \) be the number of pages Taylor read.
According to the problem statement, we can formulate the following equation based on what we know:
\[ 30 = \frac{1}{2}T + 10 \]
Now, we want to rewrite it in the form \( PX + 2 = R \). To do this, we can adjust the equation a bit.
-
Subtract 10 from both sides: \[ 30 - 10 = \frac{1}{2}T \] \[ 20 = \frac{1}{2}T \]
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Multiply both sides by 2 to eliminate the fraction: \[ 2 \cdot 20 = T \] \[ 40 = T \]
So, Taylor read 40 pages.
Now let's express the equation in the desired format \( PX + 2 = R \). We can rearrange the equation to fit this format.
Starting from: \[ 20 = \frac{1}{2}T \]
We can rewrite it as: \[ 20 - 2 = \frac{1}{2}T \]
Thus, if we let \( P = \frac{1}{2} \), \( X = T \), \( 2 = 2 \), and \( R = 20 \), we can rewrite our equation in the form:
\[ \frac{1}{2}T - 2 = 20 - 2 \]
This doesn't seem to match exactly, so we can express it as:
\[ 0.5T - 2 = 20 \]
In conclusion, from the information provided, the answer is: Taylor read 40 pages, and the equation can be represented in a form close to \( PX + 2 = R \):
\[ 0.5T - 2 = 20 \]
Where \( P = 0.5 \), \( X = T \), and \( R = 20 \).
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