A car dealer sold an average of 7 cars per day over a certain period. Excluding the day with the lowest traffic, the average number of cars sold on the remaining days was 8. Excluding the day with the highest traffic, this number was 5. Finally, if neither the lowest nor the highest traffic day is considered, the daily average is 5.75.

How many cars did the dealer sell during this period?
Solution. Let $x$ be the number of days that have passed during the sales period. Let $a$ be the number of cars sold on the weakest sales day, and $b$ be the number of cars sold on the strongest sales day. Based on the given conditions, we can write the following equations:

(1)

$$
(x-1) \cdot 8=7 x-a
$$

Similarly,

$$
(x-1) \cdot 5=7 x-b
$$

and

$$
(x-2) \cdot 5.75=7 x-(a+b)
$$

From equations (1) and (2), we get $a+b=13+x$, substituting this into (3):

$$
(x-2) \cdot 5.75=7 x-(13+x),
$$

from which $x=6$, meaning that the dealer sold $6 \cdot 7=42$ cars over the 6-day period.