SOLUTION: The sum of the digits of a two-digit number is 8. The number with the digits interchanged is 14 more than 8 times the unit digit of the original.What is the number?

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Question 566626: The sum of the digits of a two-digit number is 8. The number with the digits interchanged is 14 more than 8 times the unit digit of the original.What is the number?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the tens digit
Let +b+ = the units digit
The number is +10a+%2B+b+
given:
(1) +a+%2B+b+=+8+
The number with the digits interchanged is
+10b+%2B+a+
(2) +10b+%2B+a+=+8b+%2B+14+
(2) +a+%2B+10b+-+8b+=+14+
(2) +a+%2B+2b+=+14+
Subtract (1) from (2)
(2) +a+%2B+2b+=+14+
(1) +-a+-+b+=+-8+
+b+=+6+
and
(1) +a+%2B+b+=+8+
(1) +a+%2B+6+=+8+
(1) +a+=+8+-+6+
(1) +a+=+2+
The number is 26
check answer:
(2) +a+%2B+2b+=+14+
(2) +2+%2B+2%2A6+=+14+
(2) +2+%2B+12+=+14+
OK