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.
Excellent!
Complete the table below with the number of books, y, that Jenna has read after 3, 5, and 7 weeks. You can solve on paper and then enter your answer on Zearn.
y=5+5x

Weeks (x) Books (y)
3
5
7
You got it!
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 Jenna has read.
Weeks (x) Books (y)
3 20
5 30
7 40
Now, consider Bill. Write an equation that represents the number of comic books Bill has read, y, after x weeks.

Answer 1

To represent the number of comic books Bill has read, we can create a similar equation based on the information provided. Bill starts with 10 books and reads 5 more each week, so his equation can be written as:

\[ y = 10 + 5x \]

Where:

• \( y \) is the total number of books Bill has read after \( x \) weeks.

Now, let’s summarize the equations:

1. Jenna's Books: \( y = 5 + 5x \)
2. Bill's Books: \( y = 10 + 5x \)

Books Read by Jenna After 3, 5, and 7 Weeks

Let's find Jenna's number of books after those weeks using her equation:

• For 3 weeks: \[ y = 5 + 5(3) = 5 + 15 = 20 \]

• For 5 weeks: \[ y = 5 + 5(5) = 5 + 25 = 30 \]

• For 7 weeks: \[ y = 5 + 5(7) = 5 + 35 = 40 \]

Complete the Table for Jenna's Books

| Weeks (x) | Books (y) | |-----------|-----------| | 3 | 20 | | 5 | 30 | | 7 | 40 |

Consider For Bill

Now, you can calculate the number of books Bill has read after 3, 5, and 7 weeks using his equation:

• For 3 weeks: \[ y = 10 + 5(3) = 10 + 15 = 25 \]

• For 5 weeks: \[ y = 10 + 5(5) = 10 + 25 = 35 \]

• For 7 weeks: \[ y = 10 + 5(7) = 10 + 35 = 45 \]

Graph of the Points

Now, let's compile Bill's data after 3, 5, and 7 weeks:

| Weeks (x) | Books (y) | |-----------|-----------| | 3 | 25 | | 5 | 35 | | 7 | 45 |

You can plot these points on a graph with \( x \) (weeks) on the horizontal axis and \( y \) (books read) on the vertical axis. This will help to visualize the relationship between the number of weeks and the number of books read by both Jenna and Bill.

Finding the Week They Read the Same Number of Books

To find when both Bill and Jenna will have read the same number of books, we set their equations equal to each other:

\[ 5 + 5x = 10 + 5x \]

Since the \( 5x \) terms cancel out, this leads to:

\[ 5 = 10 \]

This means they will never read the same number of books because their reading rates are the same, but Bill started with more books (10 compared to Jenna’s 5).

If you want to find when they have the same total, you might need to graph these equations or do calculations over enough weeks to review their totals and observe at what point they get closer.

Thus, Bill will always have more books than Jenna after any number of weeks since he starts off ahead.