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A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certain green paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?
- a)2.8
- b)3.5
- c)4.2
- d)5
- e)7
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A certain violet paint contains 30 percent blue pigment and 70 percent...
From the question we know that 40 percent of the violet/green mix is blue pigment. We also know that 30 percent of the violet paint and 50 percent of the green paint is blue pigment. Since the blue pigment in the violet/green mix is the same blue pigment in the original violet and green paints, we can construct the following equation:
.3v + .5g = .4(v + g)
.3v + .5g = .4v + .4g
.1g = .1v
g = v
Therefore, the amount of violet paint is equal to the amount of green paint in the brown mixture, each contributing 50 percent of the total. Since the red pigment represents 70 percent of the weight of the vio let paint, it must account for 70 percent of 50 percent of the weight of the brown mix. This represents (.7)(.5) = .35, or 35% of the total weight of the brown mix. Since we have 10 grams of the brown paint, the red pigment must account for (.35)(10) = 3.5 grams of the brown paint.
There is an alternative way to come up with the conclusion that there must be equal amounts of green and violet paints in the mix. Since there is blue paint in both the violet and green paints, when we combine the two paints, the percentage of blue paint in the mix will be a weighted average of the percentages of blue in the violet paint and the percentage of blue in the green paint. For example, if there is twice as much violet as green in the brown mix, the percentage of blue in the violet will get double weighted. From looking at the numbers, however, 40% is exactly the simple average of the 30% blue in violet and the 50% blue in green. This means that there must be an equal amount of both paints in the mix.
Since there are equal amounts of violet and green paint in the 10 grams of brown mixture, there must be 5 grams of each. The violet paint is 70% red, so there must be (.7)(5) = 3.5 grams of red paint in the mix.
.3v + .5g = .4(v + g)
.3v + .5g = .4v + .4g
.1g = .1v
g = v
Therefore, the amount of violet paint is equal to the amount of green paint in the brown mixture, each contributing 50 percent of the total. Since the red pigment represents 70 percent of the weight of the vio let paint, it must account for 70 percent of 50 percent of the weight of the brown mix. This represents (.7)(.5) = .35, or 35% of the total weight of the brown mix. Since we have 10 grams of the brown paint, the red pigment must account for (.35)(10) = 3.5 grams of the brown paint.
There is an alternative way to come up with the conclusion that there must be equal amounts of green and violet paints in the mix. Since there is blue paint in both the violet and green paints, when we combine the two paints, the percentage of blue paint in the mix will be a weighted average of the percentages of blue in the violet paint and the percentage of blue in the green paint. For example, if there is twice as much violet as green in the brown mix, the percentage of blue in the violet will get double weighted. From looking at the numbers, however, 40% is exactly the simple average of the 30% blue in violet and the 50% blue in green. This means that there must be an equal amount of both paints in the mix.
Since there are equal amounts of violet and green paint in the 10 grams of brown mixture, there must be 5 grams of each. The violet paint is 70% red, so there must be (.7)(5) = 3.5 grams of red paint in the mix.
Most Upvoted Answer
A certain violet paint contains 30 percent blue pigment and 70 percent...
Understanding the Problem
To solve the problem, we need to determine how much red pigment contributes to the total weight of the brown paint that weighs 10 grams and contains 40% blue pigment.
Step 1: Identify the Total Blue Pigment
- The brown paint weighs 10 grams.
- Since it contains 40% blue pigment:
- Blue pigment in brown paint = 10 grams * 0.40 = 4 grams
Step 2: Determine the Blue Pigment Sources
- Violet paint contains 30% blue pigment.
- Green paint contains 50% blue pigment.
Let:
- x = weight of violet paint used (grams)
- y = weight of green paint used (grams)
Step 3: Set Up the Equations
1. Total weight equation:
- x + y = 10 grams
2. Blue pigment equation:
- 0.30x + 0.50y = 4 grams
Step 4: Solve the Equations
From the first equation, y = 10 - x. Substitute y in the second equation:
0.30x + 0.50(10 - x) = 4
Expanding and simplifying gives:
0.30x + 5 - 0.50x = 4
Combining like terms yields:
-0.20x + 5 = 4
Solving for x:
-0.20x = -1
x = 5 grams (violet paint)
Now, finding y:
y = 10 - 5 = 5 grams (green paint)
Step 5: Calculate the Red Pigment Contribution
- The violet paint has 70% red pigment.
- Red pigment in violet paint = 5 grams * 0.70 = 3.5 grams
Thus, the red pigment contributes 3.5 grams to the weight of the brown paint.
Conclusion
The correct answer is option 'B', which is 3.5 grams of red pigment.
To solve the problem, we need to determine how much red pigment contributes to the total weight of the brown paint that weighs 10 grams and contains 40% blue pigment.
Step 1: Identify the Total Blue Pigment
- The brown paint weighs 10 grams.
- Since it contains 40% blue pigment:
- Blue pigment in brown paint = 10 grams * 0.40 = 4 grams
Step 2: Determine the Blue Pigment Sources
- Violet paint contains 30% blue pigment.
- Green paint contains 50% blue pigment.
Let:
- x = weight of violet paint used (grams)
- y = weight of green paint used (grams)
Step 3: Set Up the Equations
1. Total weight equation:
- x + y = 10 grams
2. Blue pigment equation:
- 0.30x + 0.50y = 4 grams
Step 4: Solve the Equations
From the first equation, y = 10 - x. Substitute y in the second equation:
0.30x + 0.50(10 - x) = 4
Expanding and simplifying gives:
0.30x + 5 - 0.50x = 4
Combining like terms yields:
-0.20x + 5 = 4
Solving for x:
-0.20x = -1
x = 5 grams (violet paint)
Now, finding y:
y = 10 - 5 = 5 grams (green paint)
Step 5: Calculate the Red Pigment Contribution
- The violet paint has 70% red pigment.
- Red pigment in violet paint = 5 grams * 0.70 = 3.5 grams
Thus, the red pigment contributes 3.5 grams to the weight of the brown paint.
Conclusion
The correct answer is option 'B', which is 3.5 grams of red pigment.
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A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certaingreen paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixedto produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10grams, then the red pigment contributes how many grams of that weight?a)2.8b)3.5c)4.2d)5e)7Correct answer is option 'B'. Can you explain this answer?
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A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certaingreen paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixedto produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10grams, then the red pigment contributes how many grams of that weight?a)2.8b)3.5c)4.2d)5e)7Correct answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certaingreen paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixedto produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10grams, then the red pigment contributes how many grams of that weight?a)2.8b)3.5c)4.2d)5e)7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certaingreen paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixedto produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10grams, then the red pigment contributes how many grams of that weight?a)2.8b)3.5c)4.2d)5e)7Correct answer is option 'B'. Can you explain this answer?.
A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certaingreen paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixedto produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10grams, then the red pigment contributes how many grams of that weight?a)2.8b)3.5c)4.2d)5e)7Correct answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certaingreen paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixedto produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10grams, then the red pigment contributes how many grams of that weight?a)2.8b)3.5c)4.2d)5e)7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certaingreen paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixedto produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10grams, then the red pigment contributes how many grams of that weight?a)2.8b)3.5c)4.2d)5e)7Correct answer is option 'B'. Can you explain this answer?.
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A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certaingreen paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixedto produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10grams, then the red pigment contributes how many grams of that weight?a)2.8b)3.5c)4.2d)5e)7Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certaingreen paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixedto produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10grams, then the red pigment contributes how many grams of that weight?a)2.8b)3.5c)4.2d)5e)7Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certaingreen paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixedto produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10grams, then the red pigment contributes how many grams of that weight?a)2.8b)3.5c)4.2d)5e)7Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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