## Task 3 - 090713

A tourist group from the GDR consisting of exactly 100 people traveled abroad. The following information is known about this group:

(1) Exactly 10 tourists do not speak either Russian or English.

(2) Exactly 75 tourists speak Russian.

(3) Exactly 83 tourists speak English.

Determine the number of all tourists in this group who speak both languages!
From (1) it follows: Exactly 90 tourists master at least one of the two languages. Thus, according to (2), exactly $(90-75)$ people in the group speak English, but not Russian, which is 15 people.

According to (3), exactly $(90-83)$ people in the group speak Russian, but not English, which is 7 people.

Because $90-7-15=68$, it follows: Exactly 68 people master both languages.