Question

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?

Answer 1

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 ?

Answer 2

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

Answer 3

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.