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

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): You can put this solution on YOUR website!
Give variables and put the description into equations.

t and u for the tens and the ones
, the original number

Solve this linear system of equations.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

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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