let

g = Gabrielle's age, g>0

m = Mikhail's age, m>0

Gabrielle's age is two times Mikhail's age:

g = 2m

The sum of their ages is 54:

g + m = 54

by solving the system of equations:

g = 2m

g + m = 54

we find:

g = 36 years

m = 18 years

click here to see the step by step solution of the system of equations:

Mikhail's age is 18 years.