To determine the correct function that relates the variables given in your scenario, let’s first break down the details.
- You mention that the person can read about 32 pages per day.
- The usage of "105" is not initially explained, but it seems it could be a starting point or the number of pages already read.
Given this context, let's analyze the options:
- \( y = 32x + 105 \)
- \( y = 105 + 32 \)
- \( y = 32x \)
- \( y = 32x - 105 \)
In these equations:
- \( y \) likely represents the total number of pages read.
- \( x \) would represent the number of days of reading.
If we assume that 105 is the total number of pages already read (for example, the pages that do not need to be reread), then the function that relates the total pages read over time is:
Option 1: \( y = 32x + 105 \)
This correctly states that the total pages read \( y \) is equal to 32 pages per day multiplied by the number of days \( x \), plus the 105 pages that were already read.
So, if the individual reads for \( x \) days, the total pages read would indeed be 32 pages per day multiplied by the number of days plus the 105 pages they started with.
The other options are not applicable in this context:
- \( y = 105 + 32 \) does not involve a variable and just gives a number.
- \( y = 32x \) does not account for the initial 105 pages.
- \( y = 32x - 105 \) suggests a subtraction of the initial pages, which is not appropriate if they already have pages they do not need to reread.
Thus, the correct function is \( y = 32x + 105 \).