To represent the number of books Jerry has read after \( x \) weeks, we can create an equation based on the information given.
Jerry starts with 4 books and reads 6 books each week. Therefore, the equation for the number of books Jerry has read after \( x \) weeks can be expressed as:
\[ y = 4 + 6x \]
Where:
- \( y \) is the total number of books Jerry has read.
- \( 4 \) is the number of books Jerry has already read.
- \( 6 \) is the number of books Jerry reads each week.
- \( x \) is the number of weeks.
Next, we can create a similar equation for Sheila. She has read 2 books and also reads 6 books each week, so her equation would be:
\[ y = 2 + 6x \]
To find out after how many weeks they will have read the same number of books, we need to set the two equations equal to each other:
\[ 2 + 6x = 4 + 6x \]
Now, simplify this equation:
- Subtract \( 6x \) from both sides:
\[ 2 = 4 \]
This equation shows that the terms \( 6x \) cancel each other out, indicating that the two will never have read the same total number of books after any number of weeks since the equation reduces to a false statement.
Thus, Sheila will always read 2 books less than Jerry at any point in time because they both read the same amount each week. As a result, they will never have read the same number of books.