Final answer:
By setting up algebraic equations based on the information given, we determine that Jose is currently 24 years old and Naomi is currently 50 years old.
Step-by-step explanation:
To solve this age-related word problem, we can use algebra. Let's define the current age of Jose as J and the current age of Naomi as N. According to the information provided, Naomi is 26 years older than Jose, which gives us the first equation: N = J + 26.
In 9 years, the age of Jose will be J + 9, and the age of Naomi will be N + 9. The sum of their ages in 9 years will be 92, leading to our second equation: (J + 9) + (N + 9) = 92.
Substituting the first equation into the second gives us: (J + 9) + (J + 26 + 9) = 92. Simplifying this equation, we get 2J + 44 = 92. Subtracting 44 from both sides, we get 2J = 48. Dividing by 2, we find J = 24. Now that we have Jose's current age, we can use the first equation to find Naomi's current age: N = 24 + 26 = 50.
Therefore, Jose is currently 24 years old and Naomi is currently 50 years old.