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One fourth of a number exceeds one sixth of its succeeding number by 4 .find the number?
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One fourth of a number exceeds one sixth of its succeeding number by 4...
Understanding the Problem
We need to find a number that meets a specific condition: one fourth of this number exceeds one sixth of its succeeding number by 4.
Defining the Variables
- Let the unknown number be represented as "x".
- The succeeding number is then "x + 1".
Setting Up the Equation
From the problem statement, we can write the equation as follows:
- One fourth of the number: (1/4)x
- One sixth of the succeeding number: (1/6)(x + 1)
According to the problem, we can express this relationship mathematically:
- (1/4)x = (1/6)(x + 1) + 4
Solving the Equation
1. Multiply through by 12 (the least common multiple of 4 and 6) to eliminate the fractions:
- 12 * (1/4)x = 12 * (1/6)(x + 1) + 12 * 4
- 3x = 2(x + 1) + 48
2. Expand and rearrange:
- 3x = 2x + 2 + 48
- 3x = 2x + 50
- 3x - 2x = 50
- x = 50
Conclusion
The number we are looking for is 50.
Verification
To verify:
- One fourth of 50 = 12.5
- The succeeding number is 51, and one sixth of 51 = 8.5
- Now, 12.5 exceeds 8.5 by 4, confirming our solution is correct.
Thus, the final answer is 50.
We need to find a number that meets a specific condition: one fourth of this number exceeds one sixth of its succeeding number by 4.
Defining the Variables
- Let the unknown number be represented as "x".
- The succeeding number is then "x + 1".
Setting Up the Equation
From the problem statement, we can write the equation as follows:
- One fourth of the number: (1/4)x
- One sixth of the succeeding number: (1/6)(x + 1)
According to the problem, we can express this relationship mathematically:
- (1/4)x = (1/6)(x + 1) + 4
Solving the Equation
1. Multiply through by 12 (the least common multiple of 4 and 6) to eliminate the fractions:
- 12 * (1/4)x = 12 * (1/6)(x + 1) + 12 * 4
- 3x = 2(x + 1) + 48
2. Expand and rearrange:
- 3x = 2x + 2 + 48
- 3x = 2x + 50
- 3x - 2x = 50
- x = 50
Conclusion
The number we are looking for is 50.
Verification
To verify:
- One fourth of 50 = 12.5
- The succeeding number is 51, and one sixth of 51 = 8.5
- Now, 12.5 exceeds 8.5 by 4, confirming our solution is correct.
Thus, the final answer is 50.
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One fourth of a number exceeds one sixth of its succeeding number by 4 .find the number?
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One fourth of a number exceeds one sixth of its succeeding number by 4 .find the number? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about One fourth of a number exceeds one sixth of its succeeding number by 4 .find the number? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One fourth of a number exceeds one sixth of its succeeding number by 4 .find the number?.
One fourth of a number exceeds one sixth of its succeeding number by 4 .find the number? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about One fourth of a number exceeds one sixth of its succeeding number by 4 .find the number? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One fourth of a number exceeds one sixth of its succeeding number by 4 .find the number?.
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