Can you solely rely on induction to prove that your conclusion is correct

Can you decompose the numbers 20,740,6,000

Hector and alex traded video games. alex gave hector one fourth of his video games in exchange for 6 video games. then he sold 3 video games and gave 2 video games to his brother. alex ended up with 16 video games. how many video games did alex have when he started?

Solve the following pair of equations for x and y: ax/b_ by /a= a +b; ax - by = 2ab