Greg and Tina read books. Greg has read 10 books and reads 5 more each week. Tina 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 Tina has read, y, after x weeks.
Nice!
Complete the table below with the number of books, y, that Tina has read after 2, 4, and 8 weeks. You can solve on paper and then enter your answer on Zearn.
y=5+5x

Weeks (x) Books (y)
2
4
8
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 Tina has read.
Weeks (x) Books (y)
2 15
4 25
8 45
Excellent!
Now, consider Greg. Write an equation that represents the number of comic books Greg has read, y, after x weeks.
Nice!
Complete the table below with the number of books, y, that Greg has read after various numbers of weeks, x. You can solve on paper and then enter your answer on Zearn.
y=10+5x

Weeks (x) Books (y)
1
3
6

Answer 1

Let's start by establishing the equations for both Greg and Tina, which you've already done:

For Tina:

Equation:
\[ y = 5 + 5x \]
where \( y \) is the number of books Tina has read after \( x \) weeks.

Now, we can calculate the number of books Tina has read after 2, 4, and 8 weeks.

• After 2 weeks:
  \[ y = 5 + 5(2) = 5 + 10 = 15 \]

• After 4 weeks:
  \[ y = 5 + 5(4) = 5 + 20 = 25 \]

• After 8 weeks:
  \[ y = 5 + 5(8) = 5 + 40 = 45 \]

Table for Tina:

| Weeks (x) | Books (y) | |-----------|-----------| | 2 | 15 | | 4 | 25 | | 8 | 45 |

For Greg:

Equation:
\[ y = 10 + 5x \]
where \( y \) is the number of books Greg has read after \( x \) weeks.

Now, let’s calculate the number of books Greg has read after 1, 3, and 6 weeks.

• After 1 week:
  \[ y = 10 + 5(1) = 10 + 5 = 15 \]

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

• After 6 weeks:
  \[ y = 10 + 5(6) = 10 + 30 = 40 \]

Table for Greg:

| Weeks (x) | Books (y) | |-----------|-----------| | 1 | 15 | | 3 | 25 | | 6 | 40 |

Summary of Tables:

Tina's Table: | Weeks (x) | Books (y) | |-----------|-----------| | 2 | 15 | | 4 | 25 | | 8 | 45 |

Greg's Table: | Weeks (x) | Books (y) | |-----------|-----------| | 1 | 15 | | 3 | 25 | | 6 | 40 |

If you were to graph these points on a coordinate plane, you would plot the corresponding values from each table. The x-axis would represent the weeks, and the y-axis would represent the total number of books read.

Finding when they read the same number of books:

To find out when Greg and Tina will have read the same number of books, we set their equations equal to each other: \[ 10 + 5x = 5 + 5x \]

Solving for \( x \): \[ 10 - 5 = 5x - 5x \]
\[ 5 = 0 \]

Since the \( 5x \) cancels out, we see that the two will never reach the same number of books because no valid \( x \) satisfies this equation. They will always maintain a difference of 5 books.

Thus, Greg will always have 5 more books read than Tina after any number of weeks.