SOLUTION: The two digits in a 2-digit number add up to 8. If the numbers are reversed the original number is reduced by 18. Write equations to represent the situation and use a suitable meth

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Question 577216: The two digits in a 2-digit number add up to 8. If the numbers are reversed the original number is reduced by 18. Write equations to represent the situation and use a suitable method to find the original number?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = 10's digit
Let +b+ = unit's digit
given:
(1) +a+%2B+b+=+8+
(2) +10b+%2B+a++=+10a+%2B+b+-+18+
------------------------
(2) +10a+-+a+-+10b+%2B+b+=+18+
(2) +9a+-+9b+=+18+
(2) +a+-+b+=+2+
---------------
Add equations (1) and (2)
+2a+=+10+
+a+=+5+
and, since
(1) +a+%2B+b+=+8+
(1) +5+%2B+b+=+8+
(1) +b+=+3+
The original number is 53
check:
(2) +10b+%2B+a++=+10a+%2B+b+-+18+
(2) +10%2A3+%2B+5++=+10%2A5+%2B+3+-+18+
(2) +35+=+53+-+18+
(2) +35+=+35+
OK