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The numerator of a rational number is less than its denominator by 3 if the numerator become three times and the denominator is increased by 20 the new number becomes 1/8 find the original number?
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The numerator of a rational number is less than its denominator by 3 i...
Understanding the Problem
To find the original rational number, we need to set up the problem based on the information given.
Step 1: Define Variables
- Let the numerator be x.
- Let the denominator be y.
Step 2: Establish Relationships
- According to the problem, the numerator is less than the denominator by 3:
- x = y - 3
Step 3: Analyze the Conditions
- If the numerator becomes three times (3x) and the denominator is increased by 20 (y + 20), it results in:
- (3x) / (y + 20) = 1/8
Step 4: Substitute and Simplify
- Substitute x in the equation:
- (3(y - 3)) / (y + 20) = 1/8
- Simplify to get:
- 24(y - 3) = y + 20
- This leads to:
- 24y - 72 = y + 20
- 23y = 92
- y = 4
Step 5: Solve for the Numerator
- Substitute y back to find x:
- x = y - 3 = 4 - 3 = 1
Conclusion
- The original rational number is:
- 1/4
In summary, the original rational number is 1/4, derived from the relationships and conditions provided in the problem.
To find the original rational number, we need to set up the problem based on the information given.
Step 1: Define Variables
- Let the numerator be x.
- Let the denominator be y.
Step 2: Establish Relationships
- According to the problem, the numerator is less than the denominator by 3:
- x = y - 3
Step 3: Analyze the Conditions
- If the numerator becomes three times (3x) and the denominator is increased by 20 (y + 20), it results in:
- (3x) / (y + 20) = 1/8
Step 4: Substitute and Simplify
- Substitute x in the equation:
- (3(y - 3)) / (y + 20) = 1/8
- Simplify to get:
- 24(y - 3) = y + 20
- This leads to:
- 24y - 72 = y + 20
- 23y = 92
- y = 4
Step 5: Solve for the Numerator
- Substitute y back to find x:
- x = y - 3 = 4 - 3 = 1
Conclusion
- The original rational number is:
- 1/4
In summary, the original rational number is 1/4, derived from the relationships and conditions provided in the problem.
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The numerator of a rational number is less than its denominator by 3 if the numerator become three times and the denominator is increased by 20 the new number becomes 1/8 find the original number?
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The numerator of a rational number is less than its denominator by 3 if the numerator become three times and the denominator is increased by 20 the new number becomes 1/8 find the original number? 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 The numerator of a rational number is less than its denominator by 3 if the numerator become three times and the denominator is increased by 20 the new number becomes 1/8 find the original number? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The numerator of a rational number is less than its denominator by 3 if the numerator become three times and the denominator is increased by 20 the new number becomes 1/8 find the original number?.
The numerator of a rational number is less than its denominator by 3 if the numerator become three times and the denominator is increased by 20 the new number becomes 1/8 find the original number? 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 The numerator of a rational number is less than its denominator by 3 if the numerator become three times and the denominator is increased by 20 the new number becomes 1/8 find the original number? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The numerator of a rational number is less than its denominator by 3 if the numerator become three times and the denominator is increased by 20 the new number becomes 1/8 find the original number?.
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