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

Write an equation that represents the number of books Jenna has read, y, after x weeks.

Answer 1

To find when Bill and Jenna will have read the same number of books, we can set up equations for the total number of books each has read after \( x \) weeks.

1. Bill's equation:

   • Bill has read 10 books initially and reads 5 more books each week, so after \( x \) weeks, the number of books Bill has read, \( y_B \), is: \[ y_B = 10 + 5x \]

2. Jenna's equation:

   • Jenna has read 5 books initially and also reads 5 more books each week, so after \( x \) weeks, the number of books Jenna has read, \( y_J \), is: \[ y_J = 5 + 5x \]

Now, we want to find the value of \( x \) when \( y_B = y_J \).

Setting the equations equal to each other: \[ 10 + 5x = 5 + 5x \]

To solve for \( x \), we can subtract \( 5x \) from both sides: \[ 10 = 5 \]

This equation does not have a solution; it implies that Bill and Jenna will never read the same number of books because the relationship is such that the difference in their initial counts (10 for Bill and 5 for Jenna) will always be maintained due to them reading the same number of books per week.

Thus, Bill will always have 5 more books read than Jenna regardless of the number of weeks. Therefore, there will not be a number of weeks \( x \) where they will have read the same number of books.