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Practice Drill #1: Word Problems and Function Interpretation

1. The total number of pages in a book is [tex]$T$[/tex]. Eloise will read [tex]$P$[/tex] pages each day for exactly [tex][tex]$D$[/tex][/tex] days until she completes the book at the end of the final day. Which of the following expresses the relationship between these values?

A. [tex]$T = P \cdot D$[/tex]
B. [tex]$T = \frac{P}{D}$[/tex]
C. [tex][tex]$T = P + D$[/tex][/tex]
D. [tex]$T = P - D$[/tex]

Sagot :

GinnyAnswer
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).
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