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The digit in the tens place of two-digit number is three times that in the units place. If the digits are reversed, the new number will be $50,636$ less than the original number. Find the original number.

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Decimal numbers review

Full solution

Q. The digit in the tens place of two-digit number is three times that in the units place. If the digits are reversed, the new number will be

50,636

less than the original number. Find the original number.

Identify Units and Tens: Let the units digit be $x$ . Then, the tens digit is $3x$ . The original number can be expressed as $10 \times (3x) + x = 30x + x = 31x$ .
Reverse Digits: When the digits are reversed, the number becomes $10x + 3x = 13x$ .
Subtract Reversed Number: According to the problem, the original number minus the reversed number is $50636$ : $31x - 13x = 50636$ .
Simplify Equation: Simplify the equation: $18x = 50636$ .
Solve for x: Solve for x: $x = \frac{50636}{18} = 2813$ .

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