## anonymous one year ago 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?

1. amoodarya

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 ?

2. amoodarya

i type ww , w +2/3w+5/3w=70 is correct

3. mathmate

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.