Math Problem Statement
- The first digit of a four-digit natural number is 7. If this digit is transferred to the last place, a four-digit natural number will be obtained that is 864 less than the original number. Find out the original
Solution
Let the four-digit number be . Since the first digit is 7, we can express the number as:
where is the number formed by the last three digits.
When the first digit 7 is moved to the end, the new number becomes:
According to the problem, this new number is 864 less than the original number. Thus, we can write:
Substituting the expressions for and :
Simplify the equation:
Rearranging terms:
Solving for :
Thus, the original number is:
Final Answer:
The original number is 7681.
Would you like a detailed breakdown or clarification?
Here are 5 related questions for further exploration:
- How can we check the correctness of the solution?
- What happens if the first digit was a number other than 7?
- Can this logic be applied to numbers with more or fewer digits?
- What if the number obtained after transferring the digit was a specific multiple of the original?
- How would the solution change if the difference was larger than 864?
Tip: Always verify the final solution by plugging it back into the original problem conditions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
Representation of numbers in terms of place values
Basic linear equation solving
Theorems
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Suitable Grade Level
Grades 8-10
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