SOLUTION: A two-digit number is such that the sum of its digit is 1/8 of the number.
When the digits of the number are reversed and the number is subtracted from the original number, the re
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When the digits of the number are reversed and the number is subtracted from the original number, the re
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Question 1049169: A two-digit number is such that the sum of its digit is 1/8 of the number.
When the digits of the number are reversed and the number is subtracted from the original number, the result obtained is 45. Find the original number please. Found 2 solutions by josgarithmetic, MathTherapy:Answer by josgarithmetic(39617) (Show Source):
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A two-digit number is such that the sum of its digit is 1/8 of the number.
When the digits of the number are reversed and the number is subtracted from the original number, the result obtained is 45. Find the original number please.
Let the tens and units digits of the original number be T, and U, respectively
Then number is: 10T + U, and when reversed, it becomes: 10U + T
Then:
10T + U = 8(T + U) ------ Cross-multiplying
10T + U = 8T + 8U
10T - 8T = 8U - U
2T = 7U ------- eq (i)
Also, 10T + U - (10U + T) = 45
10T + U - 10U - T = 45 =====> 9T - 9U = 45 ======> 9(T - U) = 9(5) ======> T - U = 5 ======> T = 5 + U ------ eq (ii)
2(5 + U) = 7U ------ Substituting 5 + U for T in eq (i)
10 + 2U = 7U
10 = 7U - 2U
10 = 5U
U, or units digit of original number = = 2
T = 5 + 2 ------- Substituting 2 for U in eq (ii)
T, or tens digit of original number = 7
Original number:
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