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?

Question

Now, consider Bill. Write an equation that represents the number of comic books Bill has read, y, after x weeks.

Answer 1

To find out after how many weeks Bill and Jenna will have read the same number of books, we can set up an equation for each of them based on their reading habits.

1. Bill:

   • Initially has read 10 books.
   • Reads 5 more books each week.
   • After \( x \) weeks, the number of books Bill has read can be expressed as: \[ y = 10 + 5x \]

2. Jenna:

   • Initially has read 5 books.
   • Reads 5 more books each week.
   • After \( x \) weeks, the number of books Jenna has read can be expressed as: \[ y = 5 + 5x \]

Now, we need to find out when they have read the same number of books. We can set the two equations equal to each other: \[ 10 + 5x = 5 + 5x \]

Next, we can simplify this equation:

1. Subtract \( 5x \) from both sides: \[ 10 = 5 \]

2. This leads to a contradiction, meaning our current assumption leads to no solution.

However, upon careful inspection of the equations:

• The \( 5x \) term cancels out, implying that Bill will always have read more books than Jenna as long as they both read at the same rate and Bill starts with more books.

Given that Bill starts with 10 books and Jenna starts with 5, Bill will continue to have read more books than Jenna for any number of weeks.

Conclusion: Bill and Jenna will never have read the same number of books since Bill always remains ahead of Jenna.

As for the equation representing the number of comic books Bill has read after \( x \) weeks, it is: \[ y = 10 + 5x \]