Final answer:
Michael's current age is determined by translating the problem into algebraic equations and solving for his and Jane's ages. With Michael being 5 years older than Jane and the future age relationship given, we find that Michael is currently 11 years old.
Step-by-step explanation:
We can solve the given problem using algebra, where we let M represent Michael's current age, and J represent Jane's current age. Since Michael is 5 years older, we can express this relationship as M = J + 5. Four years from now, Michael will be M + 4 years old and Jane will be J + 4 years old. According to the given information, four years from now Jane will be two thirds (2/3) as old as Michael, so we can write the equation (J + 4) = 2/3(M + 4).
To find Michael's current age, we first substitute M = J + 5 into the second equation, yielding (J + 4) = 2/3((J + 5) + 4). Expanding the right side, we get (J + 4) = 2/3(J + 9). Multiplying both sides by 3 to eliminate the fraction, we have 3(J + 4) = 2(J + 9). Simplifying, we get 3J + 12 = 2J + 18. Solving for J gives us J = 18 - 12, so J = 6. Finally, since M = J + 5, we find that Michael's current age is M = 6 + 5 = 11 years.