x - blue marbles (x>0) 2x - red marbles
There are at most 36 marbles. x + 2 x ≤ 36 3 x ≤ 36 x ≤ 12 2 x ≤ 24
The greatest number of red marbles in the bag is 24.
The maximum number of red marbles in the bag is 24. This is found by setting an inequality based on the total number of marbles being at most 36 and knowing that the number of red marbles is twice the number of blue marbles. By solving the inequality, we find that there can be at most 12 blue marbles, resulting in 24 red marbles.
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