SOLUTION: The value of a certain two-digit number is eight times the sum of its digits. If the digits of the number are reversed, the result is 45 less than the original number. Find the ori

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Question 795673: The value of a certain two-digit number is eight times the sum of its digits. If the digits of the number are reversed, the result is 45 less than the original number. Find the original number.
What I tried:
x- one's digit t- ten's digit
t=8(x+t)
t-45= 1/8 x
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the tens digit
Let +u+ = the units digit
-----------------------
The actual value of the number is:
+10t+%2B+u+
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given:
(1) +10t+%2B+u+=+8%2A%28+t+%2B+u+%29+
(2) +10u+%2B+t+=+10t+%2B+u+-+45+ ( this is reversing the digits )
---------------------------
(1) +10t+%2B+u+=+8t+%2B+8u+
(1) +2t+=+7u+
(1) +t+=+%287%2F2%29%2Au+
and
(2) +10u+%2B+t+=+10t+%2B+u+-+45+
(2) +9t+-+9u+=+45+
(2) +t+-+u+=+5+
Plug (1) into (2)
(2) +%287%2F2%29%2Au+-+u+=+5+
(2) +%285%2F2%29%2Au+=+5+
(2) +u%2F2+=+1+
(2) +u+=+2+
and, since
(1) +t+=+%287%2F2%29%2A2+
(1) +t+=+7+
The original number was 72
check:
(1) +10t+%2B+u+=+8%2A%28+t+%2B+u+%29+
(1) +10%2A7+%2B+2+=+8%2A%28+7+%2B+2+%29+
(1) +72+=+8%2A9+
(1) +72+=+72+
OK
(2) +10u+%2B+t+=+10t+%2B+u+-+45+
(2) +10%2A2+%2B+7+=+10%2A7+%2B+2+-+45+
(2) +27+=+70+%2B+2+-+45+
(2) +27+=+27+
OK