Certainly! Let's break down the problem step by step to determine in how many years Jim will be twice as old as his sister Kathy.
1. Current ages:
- Jim is 9 years old.
- Kathy is 6 years younger than Jim, so Kathy is [tex]\( 9 - 6 = 3 \)[/tex] years old.
2. Future ages:
- We need to find the number of years, [tex]\( x \)[/tex], in which Jim will be twice as old as Kathy.
- In [tex]\( x \)[/tex] years, Jim’s age will be [tex]\( 9 + x \)[/tex].
- In [tex]\( x \)[/tex] years, Kathy’s age will be [tex]\( 3 + x \)[/tex].
3. Set up the equation:
- We want to find [tex]\( x \)[/tex] such that Jim is twice Kathy's age.
- This can be expressed as [tex]\( 9 + x = 2 \cdot (3 + x) \)[/tex].
4. Solve the equation:
- Start with the equation: [tex]\( 9 + x = 2 \cdot (3 + x) \)[/tex].
- Expand and simplify: [tex]\( 9 + x = 6 + 2x \)[/tex].
- Rearrange the equation to isolate [tex]\( x \)[/tex]: [tex]\( 9 - 6 = 2x - x \)[/tex].
- Simplify further: [tex]\( 3 = x \)[/tex].
So, the number of years until Jim is twice as old as Kathy is 3 years.
In summary, in 3 years, Jim will be twice as old as his sister Kathy.
