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At a certain paint store "forest green"is made by mixing 4 parts blue paint with 3 parts yellow paint."Verdant green"is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 14 liters of "forest green"to change it to "Verdant green"?
- a)2
- b)13/6
- c)3
- d)4
- e)14/3
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
At a certain paint store "forest green"is made by mixing 4 p...
To solve this problem, let's first determine the composition of "forest green" and "verdant green" in terms of blue and yellow paint.
In "forest green," the ratio of blue to yellow paint is 4:3. This means that for every 4 parts of blue paint, there are 3 parts of yellow paint. Similarly, in "verdant green," the ratio of yellow to blue paint is 4:3. Therefore, for every 4 parts of yellow paint, there are 3 parts of blue paint.
Now, let's consider the problem. We have 14 liters of "forest green" paint. Since the ratio of blue to yellow paint in "forest green" is 4:3, we can calculate the amount of blue and yellow paint in 14 liters as follows:
Blue paint: (4/7) * 14 liters = 8 liters
Yellow paint: (3/7) * 14 liters = 6 liters
Yellow paint: (3/7) * 14 liters = 6 liters
To change the color to "verdant green," we need to adjust the ratio of blue to yellow paint to 3:4. This means that for every 3 parts of blue paint, we need 4 parts of yellow paint.
Currently, we have 8 liters of blue paint in 14 liters of "forest green." Let's assume we add 'x' liters of yellow paint to achieve the desired ratio. After adding 'x' liters of yellow paint, the total amount of yellow paint will be 6 + x liters.
According to the new ratio, the amount of blue paint should be equal to 3/7 of the total paint mixture, and the amount of yellow paint should be equal to 4/7 of the total paint mixture. Therefore, we can set up the following equation:
(3/7) * (14 + x) = 8
Let's solve for 'x':
(3/7) * (14 + x) = 8
3(14 + x) = 8 * 7
42 + 3x = 56
3x = 56 - 42
3x = 14
x = 14/3
3(14 + x) = 8 * 7
42 + 3x = 56
3x = 56 - 42
3x = 14
x = 14/3
Hence, to change 14 liters of "forest green" to "verdant green," we need to add 14/3 liters of yellow paint.
Therefore, the correct answer is (E) 14/3.
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At a certain paint store "forest green"is made by mixing 4 p...
Understanding Paint Mixtures
To determine how many liters of yellow paint must be added to "forest green" to convert it into "verdant green," we first need to analyze the paint compositions.
Forest Green Composition
- "Forest green" is made by mixing:
- 4 parts blue paint
- 3 parts yellow paint
- Total parts = 4 (blue) + 3 (yellow) = 7 parts
- Thus, the proportion of blue and yellow in "forest green" can be calculated:
- Blue paint = (4/7) of total
- Yellow paint = (3/7) of total
- For 14 liters of "forest green":
- Blue paint = (4/7) * 14 = 8 liters
- Yellow paint = (3/7) * 14 = 6 liters
Verdant Green Composition
- "Verdant green" is made by mixing:
- 4 parts yellow paint
- 3 parts blue paint
- Total parts = 4 (yellow) + 3 (blue) = 7 parts
- The proportions are:
- Yellow paint = (4/7) of total
- Blue paint = (3/7) of total
Transition from Forest Green to Verdant Green
To find the final mixture's total volume after adding yellow paint, let \( x \) be the liters of yellow paint added.
- Total volume of the new mixture = \( 14 + x \) liters.
- In the new mixture, the quantity of yellow paint must satisfy:
\[
\text{Yellow paint} = \frac{4}{7} \times (14 + x)
\]
- Setting up the equation:
\[
6 + x = \frac{4}{7} \times (14 + x)
\]
- Solving for \( x \):
1. Multiply through by 7 to eliminate the fraction:
\[
7(6 + x) = 4(14 + x)
\]
\[
42 + 7x = 56 + 4x
\]
2. Rearranging gives:
\[
3x = 14 \implies x = \frac{14}{3}
\]
Conclusion
Thus, the amount of yellow paint that must be added to 14 liters of "forest green" to make "verdant green" is \( \frac{14}{3} \) liters, matching option 'E'.
To determine how many liters of yellow paint must be added to "forest green" to convert it into "verdant green," we first need to analyze the paint compositions.
Forest Green Composition
- "Forest green" is made by mixing:
- 4 parts blue paint
- 3 parts yellow paint
- Total parts = 4 (blue) + 3 (yellow) = 7 parts
- Thus, the proportion of blue and yellow in "forest green" can be calculated:
- Blue paint = (4/7) of total
- Yellow paint = (3/7) of total
- For 14 liters of "forest green":
- Blue paint = (4/7) * 14 = 8 liters
- Yellow paint = (3/7) * 14 = 6 liters
Verdant Green Composition
- "Verdant green" is made by mixing:
- 4 parts yellow paint
- 3 parts blue paint
- Total parts = 4 (yellow) + 3 (blue) = 7 parts
- The proportions are:
- Yellow paint = (4/7) of total
- Blue paint = (3/7) of total
Transition from Forest Green to Verdant Green
To find the final mixture's total volume after adding yellow paint, let \( x \) be the liters of yellow paint added.
- Total volume of the new mixture = \( 14 + x \) liters.
- In the new mixture, the quantity of yellow paint must satisfy:
\[
\text{Yellow paint} = \frac{4}{7} \times (14 + x)
\]
- Setting up the equation:
\[
6 + x = \frac{4}{7} \times (14 + x)
\]
- Solving for \( x \):
1. Multiply through by 7 to eliminate the fraction:
\[
7(6 + x) = 4(14 + x)
\]
\[
42 + 7x = 56 + 4x
\]
2. Rearranging gives:
\[
3x = 14 \implies x = \frac{14}{3}
\]
Conclusion
Thus, the amount of yellow paint that must be added to 14 liters of "forest green" to make "verdant green" is \( \frac{14}{3} \) liters, matching option 'E'.
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At a certain paint store "forest green"is made by mixing 4 parts blue paint with 3 parts yellow paint."Verdant green"is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 14 liters of "forest green"to change it to "Verdant green"?a)2b)13/6c)3d)4e)14/3Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about At a certain paint store "forest green"is made by mixing 4 parts blue paint with 3 parts yellow paint."Verdant green"is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 14 liters of "forest green"to change it to "Verdant green"?a)2b)13/6c)3d)4e)14/3Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a certain paint store "forest green"is made by mixing 4 parts blue paint with 3 parts yellow paint."Verdant green"is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 14 liters of "forest green"to change it to "Verdant green"?a)2b)13/6c)3d)4e)14/3Correct answer is option 'E'. Can you explain this answer?.
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