Problem 3. The quotient of two natural numbers is 11. If the dividend is increased by 1650, and the divisor remains the same, then the quotient will increase 7 times. What are those numbers?
Solution. If the quotient of two natural numbers is 11, and \( x \) is the divisor, then the dividend will be \( 11 x \). If the dividend is increased by 1650, the new dividend will be \( 11 x + 1650 \), so we get

$$
(11 x + 1650) : x = 7 \cdot 11
$$

i.e., \( 66 x = 1650 \), from which \( x = 25 \). The dividend will be \( 11 x = 11 \cdot 25 = 275 \). The required numbers are 25 and 275.

Problem 4. In a rectangular sports hall with a length of \( 31 \, \text{m} \) and a width of \( 21 \, \text{m} \), there is a pool. Each side of the pool is three meters away from the corresponding side of the hall. What is the area of the hall that is outside the pool?