To determine the function that correctly relates the number of pages read and the total number of pages that need to be read, let's break down the information given:
- The person reads 32 pages per day.
- There is a total of 105 pages that need to be read.
Let's define the variables:
- \( y \): the total number of pages read after \( x \) days.
- \( x \): the number of days.
Analyzing the equations
-
Equation 1: \( y = 32x + 105 \)
- In this equation, for every day \( x \), they read 32 pages, and it starts from a base of 105 pages. This interpretation implies that the total number of pages read increases by 32 each day, starting from 105. However, this interpretation seems incorrect since it would mean that they have already finished reading 105 pages before they start reading more.
-
Equation 2: \( y = 105 + 32x \)
- This equation is the same as the first one because addition is commutative; thus, it represents the same relationship. It suggests that the total number of pages read after \( x \) days includes the starting base of 105 pages plus 32 pages for each day that has passed.
Conclusion
If we interpret this as them needing to read a total of 105 pages at a rate of 32 pages per day without any pre-read pages, the function should start at 0 when no days have passed:
If the person still needs to read a total of 105 pages but reads 32 pages per day, then the relationship should correctly model:
\[ y = 105 - 32x \]
By this formula, \( y \) represents the remaining pages that need to be read after \( x \) days, starting from 105 and decreasing by 32 pages for each day.
In conclusion, neither \( y = 32x + 105 \) nor \( y = 105 + 32 \) accurately represents the scenario of reading pages towards a total. Instead, it should be formulated to track remaining pages or a cumulative model adjusted to start from zero for clarity.
3 answers