Sheila and Jerry read books. Sheila has read 2 books and reads 6 more each week. Jerry 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 Jerry has read, y, after x weeks.
Good work!
Complete the table below with the number of books, y, that Jerry 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
Nice!
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 Jerry has read.
Weeks (x) Books (y)
2 16
6 40
10 64
Excellent!
Now, consider Sheila. Write an equation that represents the number of comic books Sheila has read, y, after x weeks.

Answer 1

To represent the number of books Sheila has read after \( x \) weeks, we consider that she has read 2 books initially and reads 6 more each week. Therefore, the equation for the number of books Sheila has read, \( y \), after \( x \) weeks is:

\[ y = 2 + 6x \]

Now, let's complete the table for the number of books Sheila has read after 2, 6, and 10 weeks.

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

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

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

So, the completed table for Sheila's books is:

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

If you'd like to plot this on the coordinate plane along with Jerry's data, you now have both sets of points! For each set, make sure to label the axes clearly for weeks (x) and number of books (y).