SOLUTION: the tens digit of a two-digit number is one-half of the units digit. If the original number is reversed, the result is 9 less than twice the original number. What is the number?

Algebra ->  Expressions-with-variables -> SOLUTION: the tens digit of a two-digit number is one-half of the units digit. If the original number is reversed, the result is 9 less than twice the original number. What is the number?       Log On


   

Question 1046220: the tens digit of a two-digit number is one-half of the units digit. If the original number is reversed, the result is 9 less than twice the original number. What is the number? Solve algebraically.
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
-------------------------
(1) +t+=+%281%2F2%29%2Au+
(2) +10u+%2B+t+=+2%2A%28+10t+%2B+u+%29++-+9+
----------------------------------
(1) +u+=+2t+
Plug this result into (2)
(2) +10%2A%282t%29+%2B+t+=+2%2A%28+10t+%2B+2t+%29++-+9+
(2) +20t+%2B+t+=+2%2A%28+12t+%29+-+9+
(2) +21t+=+24t+-+9+
(2) +3t+=+9+
(2) +t+=+3+
and
(1) +u+=+2t+
(1) +u+=+2%2A3+
(1) +u+=+6+
-----------------
The number is 36
-----------------
check:
(2) +10u+%2B+t+=+2%2A%28+10t+%2B+u+%29++-+9+
(2) +10%2A6+%2B+3+=+2%2A%28+10%2A3+%2B+6+%29++-+9+
(2) +63+=+2%2A36+-+9+
(2) +63+=+72+-+9+
(2) +63+=+63+
OK