Nicole and Sebastian are reading the same book. At the beginning of the month, Nicole was on page 43 and Sebastian was on page 23. Nicole will read 3 pages per day and Sebastian will read 5 pages per day. Let NN represent the page of the book that Nicole is on at the end of tt days into the month, and let SS represent the page of the book that Sebastian is on at the end of tt days into the month. Write an equation for each situation, in terms of t, commat, and determine after how many days, t, commat, Nicole and Sebastian will be on the same page of the book.

Question

Answer
Attempt 1 out of 2

N, equalsN=
S, equalsS=
Answer:

Answer 1

To find out how many days it will take for Nicole and Sebastian to be on the same page of the book, we'll first create the equations for each of them:

1. Nicole's page number (N) after \( t \) days:

   • She starts on page 43 and reads 3 pages per day.
   • Therefore, her equation will be: \[ N = 43 + 3t \]

2. Sebastian's page number (S) after \( t \) days:

   • He starts on page 23 and reads 5 pages per day.
   • Therefore, his equation will be: \[ S = 23 + 5t \]

Next, we want to find the value of \( t \) when Nicole and Sebastian are on the same page: \[ N = S \]

Substituting the equations we found: \[ 43 + 3t = 23 + 5t \]

Now, we solve this equation for \( t \):

1. Subtract \( 3t \) from both sides: \[ 43 = 23 + 2t \]

2. Subtract 23 from both sides: \[ 20 = 2t \]

3. Divide both sides by 2: \[ t = 10 \]

Therefore, after 10 days, Nicole and Sebastian will be on the same page of the book.

In summary:

• \( N = 43 + 3t \)
• \( S = 23 + 5t \)
• Solution: \( t = 10 \)