Final answer:
Solving the algebraic equation based on Gabrielle being 14 years older than Mikhail and the sum of their ages being 114, we find that Mikhail is 50 years old.
Step-by-step explanation:
The question requires solving a simple algebra problem to determine Mikhail's age, given that Gabrielle is 14 years older than Mikhail and the sum of their ages is 114 years. To solve this, we can establish an equation with Mikhail's age being x and Gabrielle's age being x + 14. The sum of their ages is 114, providing us with the equation x + (x + 14) = 114.
Combining like terms, we get 2x + 14 = 114. Subtracting 14 from both sides gives us 2x = 100. Dividing both sides by 2, we find that x = 50, which represents Mikhail's age.
Therefore, Mikhail is 50 years old.