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 What is the total number of white marbles in BOTH bags?

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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 What is the total number of white marbles in BOTH bags?

Mathematics
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first I o for bag C w+r+b=70 \[\frac{r}{w}=\frac{2}{3} \rightarrow r=\frac{2}{3}w\\\frac{w}{b}=\frac{3}{5} \rightarrow b=\frac{5}{3}w\] now put on above equation \[w+r+b=70\\ww+\frac{2}{3}w+\frac{5}{3}w=70\\w=21\] so white marbles in bag c=21 can you solve like this for bag D ?
i type ww , w +2/3w+5/3w=70 is correct
Alternatively, we can combine the ratio to include all three colours. For Bag C r:\(\color{blue}{w}\)=2:\(\color{blue}{3}\) \(\color{blue}{w}\):b=and \(\color{blue}{3}\) :5 Since w has a matching value of 3 in both ratios, we can say r:\(\color{blue}{w}\):b=2:\(\color{blue}{3}\) :5 So \(\color{blue}{w}\) = \(\color{blue}{3}\)/(2+\(\color{blue}{3}\) +5)=3/70=21 For bag D r:\(\color{blue}{w}\)=2:3 = 8:\(\color{blue}{12}\) \(\color{blue}{w}\):b=4:5=\(\color{blue}{12}\) :15 we need to match the value for white in both ratios to combine to a single ratio (using LCM of 3 and 4=\(\color{blue}{12}\) ) We can then say r:\(\color{blue}{w}\):b=8:\(\color{blue}{12}\) :15 and the number of while marbles can be calculated in a similar way to bag C.

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