Sheila and Judy read magazines. Sheila has read 10 magazines and reads 5 more each week. Judy has read 5 magazines and reads 5 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 Judy has read, y, after x weeks.
Excellent!
Complete the table below with the number of magazines, y, that Judy has read after 3, 5, and 7 weeks. You can solve on paper and then enter your answer on Zearn.
y=5+5x

Weeks (x) Magazines (y)
3
5
7
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 magazines Judy has read.
Weeks (x) Magazines (y)
3 20
5 30
7 40
Great job!
Now, consider Sheila. Write an equation that represents the number of comic books Sheila has read, y, after x weeks

Answer 1

To create an equation that represents the number of magazines Sheila has read after \( x \) weeks, we can follow the same structure we used for Judy. Initialize the number of magazines Sheila has read:

• Sheila has read 10 magazines initially and reads 5 more each week.

Thus, the equation for the number of magazines Sheila has read, \( y \), after \( x \) weeks would be:

\[ y = 10 + 5x \]

Summary of the Equations:

• Judy: \( y = 5 + 5x \)
• Sheila: \( y = 10 + 5x \)

Finding When They Have Read the Same Number of Magazines

Now let's find out after how many weeks \( x \) they will have read the same number of magazines:

We set their equations equal to each other:

\[ 10 + 5x = 5 + 5x \]

To solve for \( x \), we can subtract \( 5x \) from both sides:

\[ 10 = 5 \]

Since this statement is not true, it indicates that they will never have read the same number of magazines as both are reading at the same rate of 5 magazines per week, but Sheila started with 5 more magazines than Judy.

Table for Judy

To complete the table for Judy's magazines after 3, 5, and 7 weeks:

1. At 3 weeks:
   \( y = 5 + 5(3) = 5 + 15 = 20 \)

2. At 5 weeks:
   \( y = 5 + 5(5) = 5 + 25 = 30 \)

3. At 7 weeks:
   \( y = 5 + 5(7) = 5 + 35 = 40 \)

Completed Table for Judy:

| Weeks (x) | Magazines (y) | |-----------|----------------| | 3 | 20 | | 5 | 30 | | 7 | 40 |

Graphing Points

The points to graph will be:

• (3, 20)
• (5, 30)
• (7, 40)

Summary

• Judy’s Equation: \( y = 5 + 5x \)
• Sheila’s Equation: \( y = 10 + 5x \)
• They will never have read the same number of magazines given their current rates.