7.1. A team of athletes, one third of whom are snowboarders, descended from the mountain. Some of them got into a cable car carriage, which can accommodate no more than 10 people, while all the others descended on their own, and their number turned out to be more than $45 \%$, but less than $50 \%$ of the total number. Determine the number of snowboarders (if it is determined from the condition of the problem ambiguously, then write in the answer the sum of all possible its values).
Answer: 5. Solution. If there were $x$ snowboarders and $y$ people descended on the cable car, then there were a total of $3 x$ athletes and $\left\{\begin{array}{l}\frac{9}{20}=\frac{45}{100}<\frac{3 x-y}{3 x}<\frac{50}{100}=\frac{10}{20}, \\ y \leq 10\end{array} \Rightarrow\right.$ $\left\{\begin{array}{l}x<\frac{20}{30} y \leq \frac{20}{3}<7, \\ y \in\left(\frac{30}{20} x ; \frac{33}{20} x\right) .\end{array}\right.$

By trying the values $x=1,2, \ldots, 6$, we find that only when $x=5$ the obtained interval $y \in\left(\frac{30}{20} x ; \frac{33}{20} x\right)$ contains an integer $(y=8)$.