Question

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

Answer 1

Let's define the number of books each person has read after \( x \) weeks.

For Greg:
- He has read 10 books initially.
- He reads 5 more books each week.
- Therefore, the total number of books Greg has read after \( x \) weeks can be expressed as:
\[
\text{Books read by Greg} = 10 + 5x
\]

For Tina:
- She has read 5 books initially.
- She also reads 5 more books each week.
- Therefore, the total number of books Tina has read after \( x \) weeks is:
\[
\text{Books read by Tina} = 5 + 5x
\]

To find out after how many weeks they will have read the same number of books, we set the equations equal to each other:
\[
10 + 5x = 5 + 5x
\]

Now, let's solve for \( x \):
1. First, we can subtract \( 5x \) from both sides:
\[
10 = 5
\]
This equation is always true, meaning there is no specific week \( x \) where their total read books will be equal; they will never have read the same number of books because both have a linear growth at the same rate. Thus, as time goes on, Greg will always have read more books than Tina by 5 books.

So, there will never be a week where they have read the same number of books.

To summarize, the equation for the number of books Tina has read after \( x \) weeks is:
\[
y = 5 + 5x
\]