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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