3. The director of the St. Petersburg Academy of Sciences, Princess E.P. Vorontsova-Dashkova, a native of Kaluga Governorate, lived for 66 years. In the 18th century, she lived 46 years longer than in the 19th century. In what year was E.R. Vorontsova-Dashkova born and in what year did she die?
3. First method of solving. Let's represent the condition of the problem in the form of a drawing

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-058.jpg?height=246&width=1282&top_left_y=1596&top_left_x=387)

1) $66-46=20$ (years) - the doubled period of time she lived in the 19th century;
2) $20: 2=10$ (years) — lived in the 19th century;
3) $46+10=56$ (years) — lived in the 18th century;
4) $1800-56=1746$ - year of birth;
5) $1800+10=1810$ - year of death.

Second method of solving (Lida Frolova, student of School No. 24).

1) $66+46=112$ (years) - would have lived Vorontsova-Dashkova if she had lived as long in the 19th century as in the 18th century;
2) $112: 2=56$ (years) — lived in the 18th century;
3) $56-46=10$ (years) - lived in the 19th century;
4) $1800-56=1746$ - year of birth;
5) $1800+10=1810$ - year of death.

Answer: $1746-1810$ years.