Theresa and Tim read books. Theresa has read 2 books and reads 6 more each week. Tim has read 4 books and reads 6 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 Tim has read, y, after x weeks.

Answer 1

To find out after how many weeks Theresa and Tim will have read the same number of books, we can set up equations representing the number of books they have read after \( x \) weeks.

1. Theresa's books: Theresa has read 2 books and reads 6 more each week. After \( x \) weeks, the number of books she has read can be expressed as: \[ T = 2 + 6x \]

2. Tim's books: Tim has read 4 books and also reads 6 more each week. After \( x \) weeks, the number of books he has read can be expressed as: \[ y = 4 + 6x \] where \( y \) represents the total number of books Tim has read after \( x \) weeks.

To find out when they will have read the same number of books, we set the two equations equal to each other: \[ 2 + 6x = 4 + 6x \]

Subtract \( 6x \) from both sides: \[ 2 = 4 \]

This equation results in a contradiction (2 does not equal 4), which means that they will never have read the same number of books since their rates of reading are the same but they started with a different number of books.

Therefore, the conclusion is that Theresa and Tim will never have read the same number of books.