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.
Great job!
Complete the table below with the number of books, y, that Tim has read after 2, 6, and 10 weeks. You can solve on paper and then enter your answer on Zearn.
y=4+6x

Weeks (x) Books (y)
2
6
10
Great job!
Next, graph the points you just found on the coordinate plane to show the relationship between x, the number of weeks, and y, the number of books Tim has read.
Weeks (x) Books (y)
2 16
6 40
10 64
Good work!
Now, consider Theresa. Write an equation that represents the number of comic books Theresa has read, y, after x weeks.

Answer 1

To write an equation representing the number of books Theresa has read, you can start by noting her initial number of books and how many she reads each week.

Theresa has read 2 books initially and reads 6 more each week. Therefore, her equation for the number of books \( y \) that she has read after \( x \) weeks would be:

\[ y = 2 + 6x \]

Next, let's complete the table for the number of books Theresa has read after 2, 6, and 10 weeks:

1. For \( x = 2 \): \[ y = 2 + 6(2) = 2 + 12 = 14 \]

2. For \( x = 6 \): \[ y = 2 + 6(6) = 2 + 36 = 38 \]

3. For \( x = 10 \): \[ y = 2 + 6(10) = 2 + 60 = 62 \]

Now, we can fill in the completed table for Theresa:

| Weeks (x) | Books (y) | |-----------|-----------| | 2 | 14 | | 6 | 38 | | 10 | 62 |

Now you have the equations and completed tables for both Tim and Theresa. Let me know if you need any further assistance!