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?

Question

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.

Answer 1

To write an equation that represents the number of magazines Jillian has read, we'll use a similar format as the equation for Dylan.

Jillian has read 2 magazines and reads 4 more each week. Thus, the equation for Jillian's magazines after \( x \) weeks is:

\[ y = 2 + 4x \]

Where:

• \( y \) is the total number of magazines Jillian has read after \( x \) weeks,
• \( 2 \) is the number of magazines she has initially read,
• \( 4x \) represents the magazines she reads over \( x \) weeks.

Now, let’s complete the table for Jillian with the number of magazines, \( y \), that she has read after 3, 6, and 9 weeks.

Table for Jillian:

\[ \begin{align*} \text{Weeks (x)} & \quad \text{Magazines (y)} \ 3 & \quad y = 2 + 4(3) = 2 + 12 = 14 \ 6 & \quad y = 2 + 4(6) = 2 + 24 = 26 \ 9 & \quad y = 2 + 4(9) = 2 + 36 = 38 \ \end{align*} \]

Completed Table:

\[ \begin{array}{|c|c|} \hline \text{Weeks (x)} & \text{Magazines (y)} \ \hline 3 & 14 \ 6 & 26 \ 9 & 38 \ \hline \end{array} \]

In summary:

• After 3 weeks, Jillian has read 14 magazines.
• After 6 weeks, she has read 26 magazines.
• After 9 weeks, she has read 38 magazines.