Asked by Lara
                The difference between the two digits of a two digit number is 2. If the digits swap places,the number is 18 less than the original number. What is the original number? 
            
            
        Answers
                    Answered by
            Reiny
            
    let the tens digit be x, then the unit digit is x-2
x ≥ 2
the value of the number is 10x + x-2
the value of the number reversed is 10(x-2) + x
10x + x-2 - ( 10(x-2) + x) = 18
11x - 2 - (11x - 20) = 18
11x - 2 - 11x + 20 = 18
18 = 18 , which is a true statement.
So it will work for any number of x
and the original number could have been:
20, 31, 42, 53, 64, 75, 86, or 97
check:
20 - 02 = 18
31 - 13 = 18
42 - 24 = 18
53 - 35 = 18
...
97 - 79 = 18
    
x ≥ 2
the value of the number is 10x + x-2
the value of the number reversed is 10(x-2) + x
10x + x-2 - ( 10(x-2) + x) = 18
11x - 2 - (11x - 20) = 18
11x - 2 - 11x + 20 = 18
18 = 18 , which is a true statement.
So it will work for any number of x
and the original number could have been:
20, 31, 42, 53, 64, 75, 86, or 97
check:
20 - 02 = 18
31 - 13 = 18
42 - 24 = 18
53 - 35 = 18
...
97 - 79 = 18
                    Answered by
            Sdsas
            
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Thx
    
Thx
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