Find all two-digit numbers with the following property: difference of that number and the number with its reversed digits is 36.

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01-07-2018
Mathematics

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Find all two-digit numbers with the following property: difference of that number and the number with its reversed digits is 36.

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konrad509 konrad509 · Answer 1 · 2018-07-01T19:26:56+02:00

konrad509 konrad509

01-07-2018

[tex]10x+y-(10y+x)=36\\ 10x+y-10y-x=36\\ 9x-9y=36\\ x-y=4\\\\ x,y\in\{1,2,3,4,5,6,7,8,9\}\\ \Downarrow\\ x=5,y=1\\ x=6,y=2\\ x=7,y=3\\ x=8,y=4\\ x=9,y=5 [/tex]

There are 5 such numbers - 51,62,73,84,95

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