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 that represents the number of books Theresa has read, \(y\), after \(x\) weeks, we need to consider how many books she has read initially and how many she reads each week.

Theresa has read 2 books and reads 6 more each week, so the equation can be represented as:

\[ y = 2 + 6x \]

Now, we can use this equation to complete the table with the number of books, \(y\), that Theresa has read after 2, 6, and 10 weeks.

Calculating Theresa's Book Count:

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

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

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

Filling Out the Table for Theresa:

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

Now we have the equation for Theresa's books and the corresponding book counts after 2, 6, and 10 weeks:

• Equation: \(y = 2 + 6x\)
• Table:

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