Bill and Jenna read books. Bill has read 10 books and reads 5 more each week. Jenna has read 5 books and reads 5 more each week. After how many weeks will they have read the same number of books?

1 answer

Let \( w \) represent the number of weeks that pass.

Bill's total number of books read after \( w \) weeks can be expressed as:

\[ 10 + 5w \]

This accounts for his initial 10 books plus 5 books read each week.

Jenna's total number of books read after \( w \) weeks can be expressed as:

\[ 5 + 5w \]

This accounts for her initial 5 books plus 5 books read each week.

To find out after how many weeks they will have read the same number of books, we set their total books read equal to each other:

\[ 10 + 5w = 5 + 5w \]

To simplify this equation, we can subtract \( 5w \) from both sides:

\[ 10 = 5 \]

This statement is false and indicates that the two will never have read the same number of books. Thus, we conclude that Bill and Jenna will not reach the same total number of books read at any point in time given the current conditions.

Hence, the answer is that they will never have read the same number of books.