Let's carefully analyze the problem step by step to identify and describe Ryan's error, and also calculate the related details including the percent of the book read each day.
### Step 1: Determine the total number of pages in the book
The book has a total of 1675 pages.
### Step 2: Determine the number of pages Ryan plans to read per day
Ryan plans to read 15 pages each day.
### Step 3: Calculate the total number of pages Ryan expects to read in 11 days
Ryan thinks he will finish the book in 11 days.
To find the total number of pages he expects to read in 11 days:
[tex]\[ \text{Pages read in 11 days} = 15 \, \text{pages/day} \times 11 \, \text{days} = 165 \, \text{pages} \][/tex]
This indicates that Ryan expects to read only 165 pages in 11 days.
### Step 4: Calculate the actual number of days needed to finish the book
To find out how many days Ryan will actually need to read the entire 1675-page book at a rate of 15 pages per day:
[tex]\[ \text{Actual days needed} = \frac{1675 \, \text{pages}}{15 \, \text{pages/day}} \approx 111.67 \, \text{days} \][/tex]
So Ryan would need approximately 112 days to finish the book (since we typically round up in the context of days).
### Step 5: Calculate the percent of the book read each day
We need to determine the percentage of the book that Ryan reads each day to the nearest tenth:
[tex]\[ \text{Percent per day} = \left( \frac{15 \, \text{pages/day}}{1675 \, \text{pages}} \right) \times 100 \approx 0.8955\% \][/tex]
Rounded to the nearest tenth, Ryan reads about 0.9% of the book each day.
### Step 6: Identify Ryan's error
Ryan's error is in his estimation of the number of days needed to finish the book. He greatly underestimated the time required. Ryan expected to finish the book in 11 days by reading 15 pages each day, but this would only allow him to read:
[tex]\[ 15 \, \text{pages/day} \times 11 \, \text{days} = 165 \, \text{pages} \][/tex]
This is far less than the total of 1675 pages, meaning he was off by:
[tex]\[ 1675 \, \text{pages} - 165 \, \text{pages} = 1510 \, \text{pages} \][/tex]
Ryan has an error in his estimation of 1510 pages, which indicates that he significantly miscalculated the duration needed to read the entire book.
### Summary
Ryan underestimated the number of days required to finish the book. He mistakenly thought he could finish it in 11 days by reading 15 pages each day, but in reality, he would need approximately 112 days to complete the 1675-page book. Each day, he reads about 0.9% of the book.
