SOLUTION: The tens digit of a positive two-digit number is larger than the units digit and neither digit is zero. The new number formed by interchanging the two digits is 54 less than the or
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Question 266536: The tens digit of a positive two-digit number is larger than the units digit and neither digit is zero. The new number formed by interchanging the two digits is 54 less than the original number. What is the sum of all possible original numbers? Answer by drk(1908) (Show Source):
You can put this solution on YOUR website! Let 10t + u be the original 2 digit number.
By interchanging the digits, we get 10u + t.
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(i)
step 1 - subtract u and then subtract t to get
(ii)
step 2 - divide by 9 to get
(iii)
So t is the set {7, 8, 9}
This makes u the set {1, 2, 3}
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our options are;
71, 82, and 93
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