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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?
- a)1
- b)3
- c)4
- d)6
- e)8
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Bag A contains red, white and blue marbles such that the red to white ...
We are told that bag B contains red and white marbles in the ration 1:4. This implies that WB, the number of white marbles in bag B, must be a multiple of 4.
What can we say about WA, the number of white marbles in bag A? We are given two ratios involving the white marbles in bag A. The fact that the ratio of red to white marbles in bag A is 1:3 implies that WA must be a multiple of 3. The fact that the ratio of white to blue marbles in bag A is 2:3 implies that WA must be a multiple of 2. Since WA is both a multiple of 2 and a multiple of 3, it must be a multiple of 6.
We are told that WA + WB = 30. We have already figured out that WA must be a multiple of 6 and that WB must be a multiple of 4. So all we need to do now is to test each candidate value of WA (i.e. 6, 12, 18, and 24) to see whether, when plugged into WA + WB = 30, it yields a value for WB that is a multiple of 4. It turns out that WA = 6 and WA = 18 are the only values that meet this criterion.
Recall that the ratio of red to white marbles in bag A is 1:3. If there are 6 white marbles in bag A, there are 2 red marbles. If there are 18 white marbles in bag A, there are 6 red marbles. Thus, the number of red marbles in bag A is either 2 or 6. Only one answer choice matches either of these numbers.
The correct answer is D.
We are told that WA + WB = 30. We have already figured out that WA must be a multiple of 6 and that WB must be a multiple of 4. So all we need to do now is to test each candidate value of WA (i.e. 6, 12, 18, and 24) to see whether, when plugged into WA + WB = 30, it yields a value for WB that is a multiple of 4. It turns out that WA = 6 and WA = 18 are the only values that meet this criterion.
Recall that the ratio of red to white marbles in bag A is 1:3. If there are 6 white marbles in bag A, there are 2 red marbles. If there are 18 white marbles in bag A, there are 6 red marbles. Thus, the number of red marbles in bag A is either 2 or 6. Only one answer choice matches either of these numbers.
The correct answer is D.
Most Upvoted Answer
Bag A contains red, white and blue marbles such that the red to white ...
To solve this problem, let's first analyze the information given in the question:
- In Bag A, the ratio of red to white marbles is 1:3.
- In Bag A, the ratio of white to blue marbles is 2:3.
- In Bag B, the ratio of red to white marbles is 1:4.
- The total number of white marbles in both bags is 30.
Let's break down the problem into steps:
1. Determine the ratio of red to white marbles in Bag A:
- The ratio of red to white marbles in Bag A is 1:3.
2. Determine the ratio of white to blue marbles in Bag A:
- The ratio of white to blue marbles in Bag A is 2:3.
3. Determine the ratio of red to white marbles in Bag B:
- The ratio of red to white marbles in Bag B is 1:4.
4. Determine the total number of white marbles in both bags:
- The total number of white marbles in both bags is given as 30.
5. Determine the number of white marbles in Bag A:
- Since the ratio of white to blue marbles in Bag A is 2:3, and the total number of white marbles in both bags is 30, we can set up the equation:
(2x + 4x) / (3x + 4x) = 30, where x is a common multiple of the ratios.
Solving this equation, we find that x = 6.
Therefore, the number of white marbles in Bag A is 2x = 2 * 6 = 12.
6. Determine the number of red marbles in Bag A:
- Since the ratio of red to white marbles in Bag A is 1:3, and we know the number of white marbles in Bag A is 12, we can set up the equation:
(1x + 3x) / (3x + 4x) = 12, where x is a common multiple of the ratios.
Solving this equation, we find that x = 4.
Therefore, the number of red marbles in Bag A is 1x = 1 * 4 = 4.
Therefore, the correct answer is option D) 4 red marbles.
- In Bag A, the ratio of red to white marbles is 1:3.
- In Bag A, the ratio of white to blue marbles is 2:3.
- In Bag B, the ratio of red to white marbles is 1:4.
- The total number of white marbles in both bags is 30.
Let's break down the problem into steps:
1. Determine the ratio of red to white marbles in Bag A:
- The ratio of red to white marbles in Bag A is 1:3.
2. Determine the ratio of white to blue marbles in Bag A:
- The ratio of white to blue marbles in Bag A is 2:3.
3. Determine the ratio of red to white marbles in Bag B:
- The ratio of red to white marbles in Bag B is 1:4.
4. Determine the total number of white marbles in both bags:
- The total number of white marbles in both bags is given as 30.
5. Determine the number of white marbles in Bag A:
- Since the ratio of white to blue marbles in Bag A is 2:3, and the total number of white marbles in both bags is 30, we can set up the equation:
(2x + 4x) / (3x + 4x) = 30, where x is a common multiple of the ratios.
Solving this equation, we find that x = 6.
Therefore, the number of white marbles in Bag A is 2x = 2 * 6 = 12.
6. Determine the number of red marbles in Bag A:
- Since the ratio of red to white marbles in Bag A is 1:3, and we know the number of white marbles in Bag A is 12, we can set up the equation:
(1x + 3x) / (3x + 4x) = 12, where x is a common multiple of the ratios.
Solving this equation, we find that x = 4.
Therefore, the number of red marbles in Bag A is 1x = 1 * 4 = 4.
Therefore, the correct answer is option D) 4 red marbles.
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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?a)1b)3c)4d)6e)8Correct answer is option 'D'. Can you explain this answer?
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