Question 551138: The sum of the digits of a certain two digit number is 5. If the number formed by interchanging the digits is subtracted from the original number the result is -9. What is the original number? Please help me solve!!!!
Answer by mathstutor458(57)   (Show Source):
You can put this solution on YOUR website! let the two digit number is xy
The sum of the digits of a certain two digit number is 5
so, x+y=5
we have only two possibilities (1,4),(2,3) vice versa we cany take because,if the number formed by interchanging the digits is subtracted from the original number the result is -9.
first take, x=1,y=4
x+y=5
1+4=5
5=5
satisfies one condition,but we have to check other condition.i.e.,If the number formed by interchanging the digits is subtracted from the original number the result is -9.
Which means, xy-yx=-9
14-41=-9 not satisfied so x=1,y=4 are not.
take, x=2,y=3
x+y=5
2+3=5
5=5
satisfies one condition,but we have to check other condition also.i.e.,If the number formed by interchanging the digits is subtracted from the original number the result is -9.
xy-yx=-9
23-32=-9
-9=-9 satisfies the condition.
so , solutions are x=2,y=3 ----->answer
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