SOLUTION: Bag C and Bag D each contain 70 marbles. All the marbles inside both bags are red, white or blue.
In bag C, R:W = 2:3 and W:B = 3:5
In bag D, R:W = 2:3 and W:B = 4:5
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-> SOLUTION: Bag C and Bag D each contain 70 marbles. All the marbles inside both bags are red, white or blue.
In bag C, R:W = 2:3 and W:B = 3:5
In bag D, R:W = 2:3 and W:B = 4:5
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Bag C and Bag D each contain 70 marbles
Bag C contains 70 marbles
(number of red marbles)+(number of white marbles)+(number of blue marbles) = total
(Rc) + (Wc) + (Bc) = 70
(Rc) + (3Rc/2) + (15Rc/6) = 70
6 = 6*70
6*(Rc) + 6*(3Rc/2) + 6*(15Rc/6) = 6*70
6Rc + 9Rc + 15Rc = 420
30Rc = 420
Rc = 420/30
Rc = 14
There are 14 red marbles in bag C
Wc = 3Rc/2
Wc = 3*14/2
Wc = 21
There are 21 white marbles in bag C
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Bag D
In bag D, R:W = 2:3 and W:B = 4:5
Bag D
Ratio 1
R:W = 2:3
Rd:Wd = 2:3
Rd/Wd = 2/3
3Rd = 2Wd
Wd = 3Rd/2
Bag D
Ratio 2
W:B = 4:5
Wd:Bd = 4:5
Wd/Bd = 4/5
5Wd = 4Bd
5(3Rd/2) = 4Bd
15Rd/2 = 4Bd
Bd = 15Rd/8
Bag D also contains 70 marbles
(number of red marbles)+(number of white marbles)+(number of blue marbles) = total
(Rd) + (Wd) + (Bd) = 70
(Rd) + (3Rd/2) + (15Rd/8) = 70
8 = 8*70
8Rd + 12Rd + 15Rd = 560
35Rd = 560
Rd = 560/35
Rd = 16
There are 16 red marbles in bag D
Wd = 3Rd/2
Wd = 3*16/2
Wd = 24
There are 24 white marbles in bag D
Wc + Wd = 21 + 24 = 45
So there are 45 white marbles total.
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