1. When a journalist asked which pairs had won the first three places in a dance competition, they received the following answers:

Svetlana: "Every girl is 3 years younger than her partner."

Igor: "All of us together were 115 years old."

Julia: "Igor and I together are 36 years old."

Anton: "Julia and I together are 40 years old."

Maksim: "The youngest among us is Ira."

Who danced with whom? Please explain your answer.
Solution. If Igor is $x$, Anton $y$, and Maxim $z$ years old, then from the condition of the problem we get the equation $x+y+z+x-3+y-3+z-3=115$, i.e., $x+y+z=62$. If Julia played with Igor, then from $x+x-3=36$ it follows that $2x=39$, which is not possible since 39 is not an even number. Similarly, if Julia played with Anton, then from $y+y-3=40$ it follows that $2y=43$. Therefore, Julia played with Maxim. According to this, $z-3+x=36$, i.e., $z+x=39$, from which it follows that $y=62-39=23$. From $z-3+y=40$ it follows that $z=20$, and from $x+y+z=115$, it follows that $x=19$. The youngest is Igor, who played with Ira, Maxim played with Julia, and Anton played with Svetlana.