Jean is six years older than her brother Wayne. Three years from now, the sum of their ages will be thirty-eight. Find their present ages.

Let's define the problem using variables and solve it step by step.

Let Wayne's current age be \( W \). Since Jean is 6 years older than Wayne, Jean's current age will be \( W + 6 \).

Three years from now, Wayne's age will be \( W + 3 \) and Jean's age will be \( (W + 6) + 3 = W + 9 \).

According to the problem, three years from now, the sum of their ages will be 38. Therefore, we can set up the following equation:

\[
(W + 3) + (W + 9) = 38
\]

### Solving the Equation:

1. Combine like terms:
   \[
   2W + 12 = 38
   \]

2. Subtract 12 from both sides:
   \[
   2W = 26
   \]

3. Divide both sides by 2:
   \[
   W = 13
   \]

So, Wayne's current age is 13 years.

Now, find Jean's age:
\[
J = W + 6 = 13 + 6 = 19
\]

So, Jean is 19 years old.

### Final Answer:
- Wayne is 13 years old.
- Jean is 19 years old.

Do you want more details or have any questions?

Here are 5 related questions to explore further:

1. What will be the sum of their ages 5 years from now?
2. How old was Jean 4 years ago?
3. If Jean was 10 years older than Wayne, what would be their current ages?
4. What was the difference in their ages 2 years ago?
5. If their age difference remains the same, what will Wayne's age be when Jean is 25?

**Tip:** When solving age problems, always account for future or past changes by adjusting both ages accordingly in the equation.

Learn how to solve the age difference problem involving Jean and Wayne. Understand the method to find their current ages using linear equations and age-related concepts. Suitable for Grades 6-8 students learning algebraic reasoning.

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