**Albert is 8 years older than his sister, Kate. In 6 years, he will be twice as old as her. How old is Kate now?**

Let Kate's current age be \( x \), and since Albert is 8 years older, his current age will be \( x + 8 \).

In 6 years, Kate's age will be \( x + 6 \), and Albert's age will be \( (x + 8) + 6 = x + 14 \).

According to the problem, in 6 years, Albert will be twice as old as Kate. Therefore, we can set up the equation:

\[
x + 14 = 2(x + 6)
\]

### Solving the equation:

1. Expand the right-hand side:
   \[
   x + 14 = 2x + 12
   \]

2. Subtract \( x \) from both sides:
   \[
   14 = x + 12
   \]

3. Subtract 12 from both sides:
   \[
   2 = x
   \]

So, Kate is currently **2 years old**.

### Verification:
- Kate is 2 years old now, so Albert is \( 2 + 8 = 10 \) years old.
- In 6 years, Kate will be \( 2 + 6 = 8 \) years old, and Albert will be \( 10 + 6 = 16 \) years old.
- Indeed, in 6 years, Albert's age (16) will be twice Kate's age (8), which confirms our solution.

Would you like more details, or do you have any questions? Here are some related questions to explore:

1. What if Albert were 10 years older than Kate?
2. What if the age difference were halved?
3. How would the problem change if it were 5 years instead of 6 years in the future?
4. What if Kate were older than Albert by a given number of years?
5. What if the relationship were based on a different multiple, like 3 times her age?

**Tip:** When solving age problems, defining variables and writing equations based on given conditions is key to solving them systematically.

Albert is 8 years older than his sister, Kate. In 6 years, he will be twice as old as her. How old is Kate now?

Learn how to solve this age-related algebra problem where Albert is 8 years older than Kate, and in 6 years, he will be twice as old as her. This step-by-step solution demonstrates how to set up and solve linear equations. Suitable for students in Grades 6-8.

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