3. In a school, in the fifth grade, 140 students study. In the sixth grade, 5% fewer students study compared to the fifth grade. The total number of students studying in the fifth and sixth grades is equal to $91 \%$ of the total number of students studying in the sixth and seventh grades, and this number is equal to $26 \%$ of the total number of students studying in this school. How many students study in the seventh grade? How many students study in this school?
Solution. In the sixth grade, 95% of the number of students in the fifth grade study, which means that in the sixth grade, there are 0.95$\cdot$140 $=133$ students. Therefore, in the fifth and sixth grades, there are a total of $140+133=273$ students. However, this number is equal to 91% of the total number of students in the sixth and seventh grades, so $273=0.91 \cdot x$, where $x$ is the total number of students in the sixth and seventh grades. Therefore, $x=\frac{273 \cdot 100}{91}=300$ students. Thus, only in the seventh grade, there are 300-133 $=167$ students. From the last condition, that 273 is 26% of the total number of students, we get that the number of students in the school is $\frac{273 \cdot 100}{26}$ $=1050$.