ratio of blue to red marbles
Another way to think about this is:
11 blue marbles = 9 red marbles
So, 1 blue marble = 9/11 red marble
(99 blue) x (9/11 red per blue) = 81 red marbles
ratio of blue to red marbles
Another way to think about this is:
11 blue marbles = 9 red marbles
So, 1 blue marble = 9/11 red marble
(99 blue) x (9/11 red per blue) = 81 red marbles
11 99 <-- Blue Marbles
-- = --
9 x <-- Red Marbles
You can cross multiply to solve for x.
11*x = 99*9
11x = 891
11/11 x = 891/11
x = 81
So if there are 99 blue marbles, to maintain the ratio, there must also be 81 red marbles.