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If x, y are positive integers and xy= 27, then what is the minimum value of 3x+4y is?
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If x, y are positive integers and xy= 27, then what is the minimum val...
Minimum Value of 3x+4y
To find the minimum value of 3x + 4y, we need to first understand the relationship between x, y, and the given condition xy = 27.
Understanding the Relationship
- Given that xy = 27, we know that x and y are factors of 27.
- The factors of 27 are 1, 3, 9, and 27. Since x and y are positive integers, the possible pairs are (1, 27), (3, 9), and (9, 3).
Calculating 3x + 4y for each pair
1. For (1, 27):
- 3(1) + 4(27) = 3 + 108 = 111
2. For (3, 9):
- 3(3) + 4(9) = 9 + 36 = 45
3. For (9, 3):
- 3(9) + 4(3) = 27 + 12 = 39
Finding the Minimum Value
- Among the calculated values, the minimum value of 3x + 4y is 39, which corresponds to the pair (9, 3).
Therefore, the minimum value of 3x + 4y when xy = 27 is 39.
To find the minimum value of 3x + 4y, we need to first understand the relationship between x, y, and the given condition xy = 27.
Understanding the Relationship
- Given that xy = 27, we know that x and y are factors of 27.
- The factors of 27 are 1, 3, 9, and 27. Since x and y are positive integers, the possible pairs are (1, 27), (3, 9), and (9, 3).
Calculating 3x + 4y for each pair
1. For (1, 27):
- 3(1) + 4(27) = 3 + 108 = 111
2. For (3, 9):
- 3(3) + 4(9) = 9 + 36 = 45
3. For (9, 3):
- 3(9) + 4(3) = 27 + 12 = 39
Finding the Minimum Value
- Among the calculated values, the minimum value of 3x + 4y is 39, which corresponds to the pair (9, 3).
Therefore, the minimum value of 3x + 4y when xy = 27 is 39.
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If x, y are positive integers and xy= 27, then what is the minimum value of 3x+4y is?
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If x, y are positive integers and xy= 27, then what is the minimum value of 3x+4y is? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If x, y are positive integers and xy= 27, then what is the minimum value of 3x+4y is? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x, y are positive integers and xy= 27, then what is the minimum value of 3x+4y is?.
If x, y are positive integers and xy= 27, then what is the minimum value of 3x+4y is? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If x, y are positive integers and xy= 27, then what is the minimum value of 3x+4y is? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x, y are positive integers and xy= 27, then what is the minimum value of 3x+4y is?.
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