Explain the steps Tessa should take to finish solving this problem. Include the answer in your response.

Question

Problem: Amelia and Oliver are both tracking how many books they read over the summer. So far, Amelia has read eight books and her goal is to read two book per week. Oliver has already read four books, and plans to read three books per week. If they meet their reading goals, after how many weeks will they have read the same number of books?

Tessa’s Solution: In x weeks, Amelia reads 2x+8 books and Oliver reads 3x+4 books. I am looking for when the number of books is the same, so I will set these two expressions equal to one another.

Answer 1

To finish solving the problem, Tessa needs to take the following steps:

1. Set the expressions equal to each other: As Tessa stated, the number of books Amelia reads after \( x \) weeks is represented by the expression \( 2x + 8 \), and the number Oliver reads is represented by \( 3x + 4 \). Therefore, Tessa needs to set up the equation:

   \[ 2x + 8 = 3x + 4 \]

2. Solve for \( x \): Next, Tessa will rearrange the equation to isolate \( x \). This can be done by moving the terms involving \( x \) to one side and the constant terms to the other side.

   • Subtract \( 2x \) from both sides:

   \[ 8 = x + 4 \]

   • Now, subtract \( 4 \) from both sides:

   \[ 4 = x \]

3. Interpret the solution: The value \( x = 4 \) indicates that after 4 weeks, both Amelia and Oliver will have read the same number of books.

4. Verification: To ensure the calculation is correct, Tessa can confirm by calculating the total books read by each after 4 weeks.

   • For Amelia: \[ 2x + 8 = 2(4) + 8 = 8 + 8 = 16 \text{ books} \]
   • For Oliver: \[ 3x + 4 = 3(4) + 4 = 12 + 4 = 16 \text{ books} \]

Both Amelia and Oliver would have read 16 books after 4 weeks, confirming that the solution is correct.

Final Answer: After 4 weeks, Amelia and Oliver will have read the same number of books.

Answer 2

put it in three paragraph

Answer 3

To solve the problem of how many weeks it will take for Amelia and Oliver to have read the same number of books, Tessa first established the expressions for the total number of books each person has read over time. Amelia, who has read 8 books and plans to read 2 books per week, can be represented by the expression \(2x + 8\) after \(x\) weeks. Oliver, who has read 4 books and aims to read 3 books each week, can be represented by the expression \(3x + 4\). Tessa understood that she needed to find the point at which these two expressions are equal.

Next, Tessa set the two expressions equal to one another: \(2x + 8 = 3x + 4\). To solve for \(x\), she moved the \(x\) terms to one side and the constant terms to the other by first subtracting \(2x\) from both sides, leading to \(8 = x + 4\). Tessa then subtracted 4 from both sides to isolate \(x\), resulting in \(x = 4\). This means that in 4 weeks, both Amelia and Oliver will have read the same number of books.

Finally, to verify her solution, Tessa calculated the total number of books read by both Amelia and Oliver after 4 weeks. For Amelia, the calculation was \(2(4) + 8 = 16\) books. For Oliver, it was \(3(4) + 4 = 16\) books as well. Since both have read 16 books after 4 weeks, Tessa confirmed that her solution was correct. Thus, the answer to the problem is that after 4 weeks, Amelia and Oliver will have read the same number of books.