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:There are 6 red marbles in Bag A.Step-by-step explanation:Bag ARed to white marble ratio is 1:3White to blue marble ratio is 2:3If we match the amount of white marbles between both ratios we can put together a three-term ratio.Red to White 2:6White to Blue 6:9Red to White to Blue 2:6:9Then, the total amount of marbles in bag A is given by:A= 2·x + 6·x + 9·xBag BB= 1·x + 4·xWhite marblesSince the two bags contain 30 white marbles:30=[tex]A_W+B_W[/tex]= 6·x + 4·x=10x ⇒ x=3Then,[tex]A_R[/tex]:red marbles in bag A[tex]A_R[/tex]=2·x=2·3=6There are 6 red marbles in Bag A.