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# digits

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The sum of the digits of a two digit positive integer is 15 , when the digits are reversed the number is 27 more than the original number . what was the original number?

Jan 31, 2021

#1
+536
+1

Possible numbers

87

78

96

69

The number has to be smaller than its opposite so

78

69

87-78=9

96-69=27

So the number is 69

Jan 31, 2021
#2
+120287
+1

Call the digits  a  and  b

So

a +  b  =  15     ⇒  b =  15  - a

So

Call  the original number  10a + (15 - a)      and call  the resulting number  10(15 - a)   + a

So     27 added to the otiginal number  = the resulting number

10a  +  ( 15 - a)   +  27 =   10 ( 15 - a)  + a

9a + 42   =  150 -  9a

18a  =   150  -  42

18a  = 108

a=  108 / 18   =   6

And  b  =15  - 6  =  9

The original number=    69

The resulting  number  =  69+ 27 =  96

Jan 31, 2021
#3
+1

Third solution:  (moomoo 's was the best !)

10b+a = 27 + 10a  + b

9b-9a=27

b+a = 15   multiply by 9  to get

9b+9a= 135       add red equations to get

18b = 162

b = 9                  then    a + 9 = 15      a = 6

69

Jan 31, 2021