Nine years from now, Jack will be three times as old as he was
eleven years ago. How old is he now?

Solve the problem. Explain your reasoning.

To solve this problem, let's define the variables and set up an equation based on the information given.

### Step-by-Step Solution

1. **Define the variable:**
   - Let \( x \) be Jack's current age.

2. **Translate the problem into mathematical expressions:**
   - "Nine years from now, Jack will be three times as old as he was eleven years ago."

   - **Nine years from now:** Jack's age will be \( x + 9 \).

   - **Eleven years ago:** Jack's age was \( x - 11 \).

   - According to the problem, nine years from now, Jack’s age \( (x + 9) \) will be three times his age eleven years ago \( 3(x - 11) \).

3. **Set up the equation:**
   \[
   x + 9 = 3(x - 11)
   \]

4. **Solve for \( x \):**

   - Distribute the 3 on the right side of the equation:
   \[
   x + 9 = 3x - 33
   \]

   - Subtract \( x \) from both sides to isolate the terms with \( x \) on one side:
   \[
   9 = 2x - 33
   \]

   - Add 33 to both sides to isolate the constant term:
   \[
   42 = 2x
   \]

   - Divide both sides by 2 to solve for \( x \):
   \[
   x = 21
   \]

5. **Conclusion:**
   - Jack is currently **21 years old**.

### Verification

To verify the solution, let's check if the conditions given in the problem are satisfied:

- **Jack’s age nine years from now:** \( x + 9 = 21 + 9 = 30 \).
- **Jack’s age eleven years ago:** \( x - 11 = 21 - 11 = 10 \).
- **Three times his age eleven years ago:** \( 3 \times 10 = 30 \).

Since \( 30 = 30 \), the solution is correct. Jack is indeed 21 years old.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. What would be Jack's age if the condition was "seven years from now, Jack will be twice as old as he was twelve years ago"?
2. If Jack was twice as old as his friend now, and nine years later he is three times as old as his friend was three years ago, how old is his friend?
3. How do you solve an age-related word problem involving more than one person?
4. What methods can be used to check the accuracy of age-related problem solutions?
5. Can age problems be solved using graphical methods?

**Tip:** When solving age-related problems, carefully translate the words into algebraic expressions and equations. This helps ensure that you accurately represent the conditions described in the problem.

Learn how to solve an age-related problem involving Jack's current age using algebraic equations and step-by-step reasoning. Jack's age problem is solved by translating words into mathematical expressions and verifying the solution. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation