Rybnikov I.g.

A store received 20 kg of cheese, and a queue formed. After selling cheese to the next customer, the saleswoman accurately calculates the average weight of the purchase for all the cheese sold and informs how many people the remaining cheese will last if everyone buys exactly this average weight. Could the saleswoman have reported after each of the first 10 customers that the cheese would last exactly 10 more people? If so, how much cheese was left in the store after the first 10 customers?

#
Let $s_{k}$ be the average weight of cheese sold to the first $k$ customers. According to the condition, $20 - k s_{k} = 10 s_{k}$, hence $s_{k} = \frac{20}{k+10}$ kg, and after the $k$-th customer, there remains

200

$k+10$

message after each customer (not limited to the first ten). After the 10th customer, exactly half of the cheese remained - 10 kg.

## Answer

It could; 10 kg.