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Divide 243into three parts such that half of the the first part,one-third of the second part and one-fourth of the third part are all equal?
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Divide 243into three parts such that half of the the first part,one-th...
let the numbers be x, y , z
So 1/2 x = 1/3 y = 1/4 z = k
x = 2k , y = 3k , z = 4k
Also,
x+y+z = 243
2k+3k+4k = 243
9k = 243
k = 27
So numbers are x = 54 , y = 81 , z = 108
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Divide 243into three parts such that half of the the first part,one-th...
Problem Statement
We need to divide 243 into three parts, let's denote them as x, y, and z. The condition is that half of the first part, one-third of the second part, and one-fourth of the third part are all equal.
Step 1: Set Up the Equations
- Let:
- Half of the first part: (1/2)x
- One-third of the second part: (1/3)y
- One-fourth of the third part: (1/4)z
- Based on the problem:
- (1/2)x = (1/3)y = (1/4)z = k (where k is a constant)
Step 2: Express Parts in Terms of k
- From the equations, we can express x, y, and z in terms of k:
- x = 2k
- y = 3k
- z = 4k
Step 3: Sum of the Parts
- Now, we add these parts:
- x + y + z = 2k + 3k + 4k = 9k
- We know the total sum is 243:
- 9k = 243
Step 4: Solve for k
- Solving for k:
- k = 243 / 9 = 27
Step 5: Find the Values of x, y, and z
- Now, substitute k back to find x, y, and z:
- x = 2k = 2 * 27 = 54
- y = 3k = 3 * 27 = 81
- z = 4k = 4 * 27 = 108
Final Result
- The three parts are:
- x = 54
- y = 81
- z = 108
Thus, 243 is divided into 54, 81, and 108, satisfying the given conditions.
We need to divide 243 into three parts, let's denote them as x, y, and z. The condition is that half of the first part, one-third of the second part, and one-fourth of the third part are all equal.
Step 1: Set Up the Equations
- Let:
- Half of the first part: (1/2)x
- One-third of the second part: (1/3)y
- One-fourth of the third part: (1/4)z
- Based on the problem:
- (1/2)x = (1/3)y = (1/4)z = k (where k is a constant)
Step 2: Express Parts in Terms of k
- From the equations, we can express x, y, and z in terms of k:
- x = 2k
- y = 3k
- z = 4k
Step 3: Sum of the Parts
- Now, we add these parts:
- x + y + z = 2k + 3k + 4k = 9k
- We know the total sum is 243:
- 9k = 243
Step 4: Solve for k
- Solving for k:
- k = 243 / 9 = 27
Step 5: Find the Values of x, y, and z
- Now, substitute k back to find x, y, and z:
- x = 2k = 2 * 27 = 54
- y = 3k = 3 * 27 = 81
- z = 4k = 4 * 27 = 108
Final Result
- The three parts are:
- x = 54
- y = 81
- z = 108
Thus, 243 is divided into 54, 81, and 108, satisfying the given conditions.
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Divide 243into three parts such that half of the the first part,one-third of the second part and one-fourth of the third part are all equal?
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Divide 243into three parts such that half of the the first part,one-third of the second part and one-fourth of the third part are all equal? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Divide 243into three parts such that half of the the first part,one-third of the second part and one-fourth of the third part are all equal? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Divide 243into three parts such that half of the the first part,one-third of the second part and one-fourth of the third part are all equal?.
Divide 243into three parts such that half of the the first part,one-third of the second part and one-fourth of the third part are all equal? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Divide 243into three parts such that half of the the first part,one-third of the second part and one-fourth of the third part are all equal? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Divide 243into three parts such that half of the the first part,one-third of the second part and one-fourth of the third part are all equal?.
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