Janet s three years older that her sister Julie. Janet's brother is eight years younger than their sister Julie. The sum of all their ages is 55 year.

Let's solve this problem step by step by defining the ages of Janet, Julie, and their brother.

1. **Let \( x \) represent Julie's age**.

2. Since Janet is three years older than Julie, Janet's age would be \( x + 3 \).

3. Janet's brother is eight years younger than Julie, so his age would be \( x - 8 \).

4. According to the problem, the sum of all their ages is 55 years. Therefore, we can write the equation:
   \[
   \text{Julie's age} + \text{Janet's age} + \text{Brother's age} = 55
   \]
   Substituting the expressions for their ages:
   \[
   x + (x + 3) + (x - 8) = 55
   \]

5. Combine the like terms:
   \[
   3x - 5 = 55
   \]

6. Solve for \( x \):
   \[
   3x = 60
   \]
   \[
   x = 20
   \]

So, **Julie is 20 years old**.

Now, we can find the ages of Janet and her brother:
- Janet's age: \( x + 3 = 20 + 3 = 23 \) years
- Brother's age: \( x - 8 = 20 - 8 = 12 \) years

### Final Answer:
- Julie is **20 years old**.
- Janet is **23 years old**.
- Their brother is **12 years old**.

Would you like more details on any part of this solution, or do you have any other questions?

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**Related Questions:**
1. What would be the sum of their ages in 5 years?
2. If Julie was 2 years older, what would be the new sum of their ages?
3. How would the equation change if Janet was instead 5 years older than Julie?
4. What if the sum of their ages was 65 years, how would their ages change?
5. How can you express Janet's brother's age in terms of Janet's age?

**Tip:** When solving word problems, always start by defining variables for the unknown quantities and then write equations based on the relationships given in the problem.

Janet is three years older than her sister Julie. Janet's brother is eight years younger than their sister Julie. The sum of all their ages is 55 years.

Solve this age problem where Janet is three years older than Julie, and their brother is eight years younger than Julie. The sum of their ages is 55 years. Learn step-by-step how to form and solve the linear equation to find their ages, suitable for Grades 6-8.

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