15. (6 points) There are three buckets, A, B, and C, each containing some oil. First, $\frac{1}{3}$ of the oil in bucket A is poured into bucket B, then $\frac{1}{5}$ of the oil in bucket B is poured into bucket C. At this point, the oil in the three buckets is the same. If bucket C initially had 48 kilograms of oil, then initially bucket A had $\qquad$ kilograms of oil, and bucket B had $\qquad$ kilograms of oil.
【Solution】Solution: Assume that after bucket A pours oil into bucket B, the oil in bucket B is 5 parts, and it gives $\frac{1}{5}$ to bucket C, resulting in both buckets having the same amount, which means bucket C originally had 3 parts;
When all three buckets have the same amount, they each have 4 parts, which means that after bucket A pours out one-third, it still has 4 parts, so it originally had 6 parts;

After bucket A pours 2 parts of oil into bucket B, the oil in bucket B is 5 parts, indicating that bucket B originally also had 3 parts, so the 3 parts in bucket C are equivalent to 48 kilograms, with each part being $48 \div 3=16$ (kilograms). Therefore, the initial amount of oil in bucket A should be $16 \times 6=96$ (kilograms), and in bucket B, it should be $16 \times 3=48$ (kilograms). Therefore, the answers are: 96, 48.