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.

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: \[ y = 5 + 5x \]