To determine the correct relationship between the total number of pages [tex]\( T \)[/tex], the pages read per day [tex]\( P \)[/tex], and the number of days [tex]\( D \)[/tex], we need to think logically about the scenario described.
Eloise reads [tex]\( P \)[/tex] pages each day and she does this for [tex]\( D \)[/tex] days. The total number of pages read each day accumulates over the [tex]\( D \)[/tex] days. The key here is to understand that total reading over multiple days involves multiplication since reading happens repeatedly each day.
Here is a detailed step-by-step solution:
1. Identify the key variables:
- [tex]\( T \)[/tex]: Total number of pages in the book.
- [tex]\( P \)[/tex]: Number of pages Eloise reads each day.
- [tex]\( D \)[/tex]: Number of days Eloise reads.
2. Understand the problem context:
- Eloise reads [tex]\( P \)[/tex] pages each day.
- She reads for [tex]\( D \)[/tex] days.
- At the end of [tex]\( D \)[/tex] days, she has finished the book with [tex]\( T \)[/tex] pages in total.
3. Set up the relationship:
- Each day she reads [tex]\( P \)[/tex] pages.
- Therefore, in [tex]\( D \)[/tex] days, she will read [tex]\( P \)[/tex] pages each day for [tex]\( D \)[/tex] days.
4. Determine how reading [tex]\( P \)[/tex] pages for [tex]\( D \)[/tex] days adds up to the total pages [tex]\( T \)[/tex]:
- If she reads [tex]\( P \)[/tex] pages each day for exactly [tex]\( D \)[/tex] days, the total number of pages read is the product of the number of pages she reads each day and the number of days.
- This leads us to multiply the number of pages per day by the number of days: [tex]\( P \times D \)[/tex].
Therefore, the relationship between these variables that expresses the total number of pages [tex]\( T \)[/tex] is given by:
[tex]\[ T = P \times D \][/tex]
5. Choose the correct option:
- (A) [tex]\( T = P \times D \)[/tex] is indeed correct.
- (B), (C), and (D) do not accurately reflect the described relationship.
So, the correct expression is option (A):
[tex]\[ T = P \times D \][/tex]
Thus, the correct answer is (A).
