2. (8 points) Shuaishuai memorized more than a hundred words in seven days. The ratio of the number of words memorized in the first three days to the number of words memorized in the last four days is $3: 4$, and the ratio of the number of words memorized in the last three days to the number of words memorized in the first four days is 5:6; then, Shuaishuai memorized $\qquad$ words on the fourth day.
【Solution】Solution: According to the analysis, let the number of words memorized in the first three days be $3k$, then the number of words memorized in the following four days be $4k$, and the number of words memorized on the fourth day be $a$, then the number of words memorized in the last three days be $4k-a$,
According to the problem, we have: $\frac{4k-a}{4k}=\frac{5}{6}$, solving this gives: $a=\frac{9}{11}k$,
Therefore, the number of words memorized in the last three days is: $4k-\frac{9}{11}k=\frac{35}{11}k$, hence: the ratio of the number of words memorized in the first three days, the fourth day, and the last three days is: $3k: \frac{9}{11}k: \frac{35}{11}k=33: 9: 35$,
Let the number of words memorized in the first three days, the fourth day, and the last three days be: $33b, 9b, 35b$, then the total number of words memorized in seven days is: $33b+9b+35b=77b$,
$\because 100<77b<200 \therefore b=2$, that is: the number of words memorized on the fourth day is: $9 \times 2=18$.
Therefore, the answer is: 18.