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

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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.