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
Nice!
The line represents the equation you graphed earlier, showing the number of books Tina has read, y, after x weeks. Use the points that you just found to graph the equation for Greg on this same graph.
Weeks (x) Books (y)
1 15
3 25
6 40
Nice!
Is there a time when Greg and Tina have read the same number of books?
x
y
Gr
Ti
0
1
2
3
4
5
6
7
8
9
10
0
5
10
15
20
25
30
35
40
45
50
Weeks
Books read
a time when they have read the same number of books.

We can see this on the graph

Answer 1

To determine when Greg and Tina will have read the same number of books, let's analyze the equations and the information provided.

1. Equations for Books Read:

   • For Tina: \( y_T = 5 + 5x \) (where \( x \) is the number of weeks)
   • For Greg: \( y_G = 10 + 5x \)

2. Set the Equations Equal to Each Other to find when they have read the same number of books: \[ 5 + 5x = 10 + 5x \]

3. Solve for \( x \):

   • When you simplify this equation, you will notice that the \( 5x \) terms cancel out: \[ 5 = 10 \] This implies there is no solution, which means Greg and Tina will never have read the same number of books because they read at the same rate (5 books per week), but Greg started with 10 books while Tina started with only 5. Thus, Greg will always have 5 more books than Tina no matter how many weeks pass.

4. Table for Tina's Books: Using the provided equation for Tina:

• For \( x = 2 \): \[ y = 5 + 5(2) = 5 + 10 = 15 \]
• For \( x = 4 \): \[ y = 5 + 5(4) = 5 + 20 = 25 \]
• For \( x = 8 \): \[ y = 5 + 5(8) = 5 + 40 = 45 \]

So the completed table for Tina is:

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

5. Table for Greg's Books: Using the provided equation for Greg:

• For \( x = 1 \): \[ y = 10 + 5(1) = 10 + 5 = 15 \]
• For \( x = 3 \): \[ y = 10 + 5(3) = 10 + 15 = 25 \]
• For \( x = 6 \): \[ y = 10 + 5(6) = 10 + 30 = 40 \]

So the completed table for Greg is:

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

6. Graphing the Points: You would graph Tina's points (2, 15), (4, 25), (8, 45) and Greg's points (1, 15), (3, 25), (6, 40) on the same coordinate plane.

7. Conclusion: As noted, Greg and Tina will never have the same number of books read, since Greg always starts with 5 more books than Tina and they both read at the same rate. The graph will show parallel lines, reflecting their constant difference in the number of books read.