Andrew's age is three times John's plus nine years, and their ages add up to 69 years. Find both ages.

Solution:
1. Define variables:
- Let x be Juan's age.
- Andrés' age is then 3x + 9.

2. Set up the equation for the total age:
- Juan's age x plus Andrés' age 3x + 9 equals 69.

3. Equation:
x + (3x + 9) = 69

4. Simplify and solve for x:
x + 3x + 9 = 69
4x + 9 = 69
4x = 60
x = 15

5. Find Andrés' age:
- Substitute x = 15 into Andrés' age expression:
3x + 9 = 3(15) + 9 = 45 + 9 = 54

6. Therefore, the ages are:
- Juan: 15 years
- Andrés: 54 years