Problem Solving

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?

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Bag A--- R : W = 2:6 and W : B = 6:9 so it is 2x:6x:9x = R:W:B
Bag B--- R : W = 1y:4y

given 6x+4y = 30 what is the value of 2x?
possible values of x and y: x=3,y=3 and y=6,x=1

Number of redballs = 2x = 6 or 2

Using options only 6 is there...

cuty wrote: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?

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We've seen a good algebraic solution, so let's attack the question strategically, by backsolving.

When the answer choices are numbers and the question is simple (e.g. "how many red marbles could there be?"), then backsolving is often a very effective approach.

If you can't quickly eliminate some choices via logic/common sense, then start with either B or D. Let's try B.

If there are 3 red marbles in the first bag, then there must be 9 white marbles. If there are 9 white marbles, then there must be 13.5 blue marbles. Well heck, we can't have 1/2 a marble, so eliminate B. We saw that an odd value for red gave us a bad result, so let's get rid of A as well.

Next let's check D. If there are 6 red marbles in bag A, then there are 18 white marbles. 18 white marbles means 27 blue marbles, which is legal.

On to bag B! 18 white marbles in bag A means we have 12 white marbles in bag B (for our total of 30 white). Since 12 is a multiple of 4, we can satisfy our 1:4 ratio for bag B. Accordingly, 6 works - choose D!