Final answer:
Leo has 2574 red marbles.
Step-by-step explanation:
Let's say that the number of blue marbles Leo has is x. According to the given information, Leo has 9 times as many red marbles as blue marbles. So the number of red marbles Leo has is 9x.
It is also given that he has 2288 more red marbles than blue marbles, which means 9x = x + 2288.
Simplifying the equation, we can subtract x from both sides: 8x = 2288. Dividing both sides by 8, we find that x = 286.
Therefore, Leo has 9 times 286 red marbles, which equals 2574 red marbles.