SOLUTION: The sum of the digits of a two-digit number is 15. if the digits are interchanged the new number minus the original number is equal to -9 . find the original number.

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Question 1031450: The sum of the digits of a two-digit number is 15. if the digits are interchanged the new number minus the original number is equal to -9 . find the original number.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 2 digits be:
+u+ for the units digit
+t+ for the tens digit
-----------------------
(1) +u+%2B+t+=+15+
-----------------------
The VALUE of the original number
is: +10t+%2B+u+
When you interchange the digits, the
VALUE of the new number becomes:
+10%2Au+%2B+t+
----------------------------
(2) +10u+%2B+t+-+10t+-+u+=+-9+
-----------------------------
(2) +9u+-+9t+=+-9+
(2) +u+-+t+=+-1+
--------------------
Add (1) and (2)
(2) +u+-+t+=+-1+
(1) +u+%2B+t+=+15+
------------------
+2u+=+14+
+u+=+7+
and
(2) +u+-+t+=+-1+
(2) +7+-+t+=+-1+
(2) +t+=+8+
-----------------
The original number is 87
-----------------------
check answer:
The sum of the digits of a two-digit number is 15
+8+%2B+7+=+15+
OK
If the digits are interchanged the new number
minus the original number is equal to -9
+78+-+87+=+-9+
+-9+=+-9+
OK