SOLUTION: The value of a certain two-digit number is 9 times the sum of its digits. If the digits are reversed, the resulting number is 63 then the original number. Find the original number.

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Question 226203: The value of a certain two-digit number is 9 times the sum of its digits. If the digits are reversed, the resulting number is 63 then the original number. Find the original number.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the units digit beu
Let the tens digit be t
given:
(1) 10t+%2B+u+=+9%2A%28t+%2B+u%29
(2) 10u+%2B+t+=+10t+%2B+u+-+63
-------------------------
(1) 10t+%2B+u+=+9t+%2B+9u%29
t+=+8u
and
(2) 10u+%2B+t+=+10t+%2B+u+-+63
10u+%2B+8u+=+10%2A8u+%2B+u+-+63
18u+=+81u+-+63
81u+-+18u+=+63
63u+=+63
u+=+1
and
t+=+8u
t+=+8%2A1
t+=+8
The original number is 81
check:
(1) 10t+%2B+u+=+9%2A%28t+%2B+u%29
10%2A8+%2B+1+=+9%2A%288+%2B+1%29
81+=+9%2A9
81+=+81
(2) 10u+%2B+t+=+10t+%2B+u+-+63
10%2A1+%2B+8+=+10%2A8+%2B+1+-+63
18+=+81+-+63
18+=+18
OK