Question

Jillian and Dylan read magazines. Jillian has read 2 magazines and reads 4 more each week. Dylan has read 6 magazines and reads 4 more each week. After how many weeks will they have read the same number of magazines?
Write an equation that represents the number of magazines Dylan has read, y, after x weeks.
Excellent!
Complete the table below with the number of magazines, y, that Dylan has read after 3, 6, and 9 weeks. You can solve on paper and then enter your answer on Zearn.
y=6+4x

Weeks (x) Magazines (y)
3
6
9
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 magazines Dylan has read.
Weeks (x) Magazines (y)
3 18
6 30
9 42
Great job!
Now, consider Jillian. Write an equation that represents the number of comic books Jillian has read, y, after x weeks.
You got it!
Complete the table below with the number of magazines, y, that Jillian has read after various numbers of weeks, x. You can solve on paper and then enter your answer on Zearn.
y=2+4x

Weeks (x) Magazines (y)
1
4
7
Good work!
The line represents the equation you graphed earlier, showing the number of magazines Dylan has read, y, after x weeks. Use the points that you just found to graph the equation for Jillian on this same graph.
Weeks (x) Magazines (y)
1 6
4 18
7 30
Great job!
Is there a time when Jillian and Dylan have read the same number of magazines?
x
y
Ji
Dy
0
1
2
3
4
5
6
7
8
9
10
0
6
12
18
24
30
36
42
48
54
60
Weeks
Magazines read
a time when they have read the same number of magazines.

We can see this on the graph

Answer 1

Let's summarize the information we have and then find the solution to the question about when Jillian and Dylan have read the same number of magazines.

### Equations:
- **Dylan's magazines**: \( y = 6 + 4x \)
- **Jillian's magazines**: \( y = 2 + 4x \)

### Steps to find when they read the same number of magazines:

1. Set the equations equal to each other to find \( x \):
\[
6 + 4x = 2 + 4x
\]

2. Subtract \( 4x \) from both sides:
\[
6 = 2
\]
This statement indicates that the number of magazines read per week at a constant rate for both Dylan and Jillian is the same (4 magazines per week). Since they started reading at different initial values, we will check their number of magazines for different values of \( x \):

### Calculating magazines read for Jillian and Dylan after a certain number of weeks:

| Weeks (x) | Dylan's magazines (y) | Jillian's magazines (y) |
|-----------|------------------------|--------------------------|
| 0 | 6 | 2 |
| 1 | 10 | 6 |
| 2 | 14 | 10 |
| 3 | 18 | 14 |
| 4 | 22 | 18 |
| 5 | 26 | 22 |
| 6 | 30 | 26 |
| 7 | 34 | 30 |
| 8 | 38 | 34 |
| 9 | 42 | 38 |
| 10 | 46 | 42 |
| 11 | 50 | 46 |
| 12 | 54 | 50 |
| 13 | 58 | 54 |
| 14 | 62 | 58 |
| 15 | 66 | 62 |

From the table, we can see that both will have read the same number of magazines when \( x = 15 \) weeks.

### Summary:
After **15 weeks**, both Jillian and Dylan will have read the same number of magazines.