To find out after how many weeks Greg and Rick will have read the same number of comic books, we can start by defining their reading progress with equations.
For Greg:
- Greg has read 2 comic books and reads 2 more each week.
- Therefore, the number of comic books Greg has read after \( x \) weeks is:
\[ G(x) = 2 + 2x \]
For Rick:
- Rick has read 5 comic books and also reads 2 more each week.
- Therefore, the number of comic books Rick has read after \( x \) weeks is:
\[ R(x) = 5 + 2x \]
Setting up the equation:
We want to find the number of weeks \( x \) where they have read the same number of comic books:
\[ G(x) = R(x) \]
Substituting the expressions we derived, we have:
\[ 2 + 2x = 5 + 2x \]
Solving the equation:
To solve for \( x \), we can simplify the equation:
- Subtract \( 2x \) from both sides:
\[ 2 = 5 \]
This equation indicates that the linear terms \( 2x \) cancel each other out, and we are left with a contradiction, which shows that the initial conditions set by the equations makes it impossible for Greg and Rick to ever have read the same number of comic books.
Conclusion:
The conclusion based on the derived equations is that Greg will never have read the same number of comic books as Rick, no matter how many weeks pass, since they both have the same reading rate of 2 comic books per week but started with different amounts.