SOLUTION: The sum of the digits of a two-digit counting number is 10. If the digits are reversed, the new number is one less that twice the original number. What is the original number?
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Question 625310: The sum of the digits of a two-digit counting number is 10. If the digits are reversed, the new number is one less that twice the original number. What is the original number?
(please help by showing work.)
Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
Let the number "ab"
Reversed number = "ba"
a+b=10
10b+a = 2(10a+b)-1
10b+a = 20a+2b-1
10b+a -20a -2b +1 =0
-19a+8b+1=0
Since b = 10-a
-19a+8(10-a)+1=0
-19a+80-8a+1=0
-27a=-81
a = 3
b=7
Answer: original number is 37
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