Question

Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 30 white marbles. How many red marbles could be in bag A?

Answer 1

There are 6 red marbles in Bag A.

Explanation:

Bag A

Red to white marble ratio is 1:3

White to blue marble ratio is 2:3

If we match the amount of white marbles between both ratios we can put together a three-term ratio.

Red to White 2:6

White to Blue 6:9

Red to White to Blue 2:6:9

Then, the total amount of marbles in bag A is given by:

A= 2·x + 6·x + 9·x

Bag B

B= 1·x + 4·x

White marbles

Since the two bags contain 30 white marbles:

30=
`A_W+B_W`= 6·x + 4·x=10x ⇒ x=3

Then,

`A_R`:red marbles in bag A

`A_R`=2·x=2·3=6

There are 6 red marbles in Bag A.