You have enough information to figure out the number of red and green marbles:
From "350 marbles" and "40% of them were red": 350*0.40 = 140 red
10% more red than green: g + 0.10*g = 140 --> 1.10g = 140 --> g = 140/1.1 = 127.27 (this is a problem, marbles must come in whole numbers).
In this sense, the problem can not be solved. That is, you generally count marbles in whole units, so a fractional number of green marbles makes no sense.
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Below is an EXAMPLE problem that can be solved
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If there were 330 marbles total, you'd have 0.4*330 = 132 red, 132/1.1 = 120 green, and then you could say (orange) + (white) = 78 ( 78 = 330-132-120)
Since we are also told (white) = 2*(orange) we can re-write the (orange)+(white) equation as
(orange) + 2*(orange) = 78
3*(orange) = 78 ---> orange = 26
and (white) = 2*(26) = 52
# red = 132
# green = 120
# white = 52
# green = 26
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Total = 330 So, for 330 marbles, the problem works, but not for 350.
The given total number of marbles must be divisible by 3, 10, and 11 in order for the problem to work out (330, 660, etc.).
