https://file.aiquickdraw.com/mathbot/file/1725446087884l3ayvizf.jpg

The problem in the image is in Japanese. Here's the translation:

"Currently, the brother is 16 years old, and the sister is 12 years old. When will the brother's age be three times the sister's age?"

Let's solve this step by step.

### Variables:
- Brother's current age = 16 years
- Sister's current age = 12 years

Let's assume after \( x \) years, the brother's age will be three times the sister's age.

### Future Ages:
- Brother's age after \( x \) years = \( 16 + x \)
- Sister's age after \( x \) years = \( 12 + x \)

### Equation:
We are told that at that time, the brother's age will be three times the sister's age:
\[
16 + x = 3(12 + x)
\]

### Solve the Equation:
\[
16 + x = 36 + 3x
\]
\[
16 - 36 = 3x - x
\]
\[
-20 = 2x
\]
\[
x = -10
\]

### Interpretation:
Since \( x = -10 \), this indicates that the brother's age was three times the sister's age 10 years ago.

- 10 years ago:
  - Brother's age: \( 16 - 10 = 6 \) years
  - Sister's age: \( 12 - 10 = 2 \) years

Indeed, \( 6 = 3 \times 2 \), so the solution is correct.

Would you like more details or have any further questions? Here are some related questions:

1. What would be the ratio of their ages 5 years from now?
2. How old was the sister when the brother was twice her age?
3. Can you derive a general formula for when one sibling's age will be a multiple of the other’s age?
4. How does the difference in age affect the calculation?
5. What if the problem asked for the sister’s age to be a specific fraction of the brother’s age?

**Tip:** When dealing with age problems, setting up the correct equation based on the relationships described is key to solving the problem efficiently.

Currently, the brother is 16 years old, and the sister is 12 years old. When will the brother's age be three times the sister's age?

Solve the problem where a brother is currently 16 years old, and his sister is 12. Discover when the brother's age will be three times the sister's age using linear equations. Suitable for students in Grades 6-8.

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