3.50 Ann and Barbara compare their ages, and find that the current age of B is the same as the age of A in a certain past year, in a certain past year B and A were the same age in a previous year, in a previous year, B was half the age of A this year. If the sum of their current ages is 44 years, then the age of A is
(A) 22.
(B) 24.
(C) 25.
(D) 26.
(E) 28.
(27th American High School Mathematics Examination, 1976)
[Solution] Let $A$ be Ann's current age, and $B$ be Barbara's current age. Then $B = A - t$, where $t$ satisfies $B - t = A - T$, and here $T$ satisfies $B - T = \frac{1}{2} A$. Also, since $A + B = 44$, we get the system of equations for $A, B, t$, and $T$:
$$
\left\{\begin{array}{l}
A + B = 44, \\
A - B - t = 0, \\
A - B + t - T = 0, \\
A - 2 B + 2 T = 0 .
\end{array}\right.
$$

Express $B$ and $t$ in terms of $A$ using the first two equations, and substitute the results into the last two equations to get
$$
A = 24 \text{.}
$$

Therefore, the answer is $(B)$.