Bill and Amy read comic books. Bill has read 2 comic books and reads 6 more each week. Amy has read 4 comic books and reads 6 more each week. After how many weeks will they have read the same number of comic books?

Question

Write an equation that represents the number of comic books Amy has read, y, after x weeks.

Answer 1

Let's define the situation with equations.

1. Bill's Comic Books:

   • Bill starts with 2 comic books and reads 6 more each week.
   • The equation for the number of comic books Bill has read after \( x \) weeks can be represented as: \[ B = 2 + 6x \]

2. Amy's Comic Books:

   • Amy starts with 4 comic books and also reads 6 more each week.
   • The equation for the number of comic books Amy has read after \( x \) weeks can be represented as: \[ A = 4 + 6x \]

Next, we want to find the number of weeks \( x \) after which the number of comic books they have read will be the same, i.e., \( A = B \).

Setting the two equations equal to each other: \[ 2 + 6x = 4 + 6x \]

Now, we can solve for \( x \): \[ 2 + 6x = 4 + 6x \] Subtract \( 6x \) from both sides: \[ 2 = 4 \]

This results in a contradiction, suggesting that they will never have read the same number of comic books since their reading rates are the same and they started with different initial amounts.

Summary:

• The equations representing the number of comic books read:
  • Bill: \( B = 2 + 6x \)
  • Amy: \( A = 4 + 6x \)
• They will never reach the same number of comic books read.