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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?

Respuesta :

valenbraca

Answer:

There are 6 red marbles in Bag A.

Step-by-step 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=[tex]A_W+B_W[/tex]= 6·x + 4·x=10x ⇒ x=3

Then,

[tex]A_R[/tex]:red marbles in bag A

[tex]A_R[/tex]=2·x=2·3=6

There are 6 red marbles in Bag A.

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