SOLUTION: The ones digit of a number is 1 more than twice the tens digit. If the digits are reversed, the new number is 8 less than 3 times the original number. What is the original number?

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: The ones digit of a number is 1 more than twice the tens digit. If the digits are reversed, the new number is 8 less than 3 times the original number. What is the original number?       Log On


   

Question 915117: The ones digit of a number is 1 more than twice the tens digit. If the digits are reversed, the new number is 8 less than 3 times the original number. What is the original number? Thanks in advance, and please do hurry up, I need to submit it soon.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the original number
+10t+%2B+u+ where:
+t+ = the tens digit
+u+ = the units digit
-----------------------
given:
(1) +u+=+2t+%2B+1+
(2) +10u+%2B+t+=+3%2A%28+10t+%2B+u+%29+-+8+
-------------------------------
(2) +10u+%2B+t+=+30t+%2B+3u+-+8+
(2) +7u+=+29t+-+8+
----------------------
Substitute (1) into (2)
(2) +7%2A%28+2t+%2B+1+%29+=+29t+-+8+
(2) +14t+%2B+7+=+29t+-+8+
(2) +15t+=+15+
(2) +t+=+1+
and
(1) +u+=+2t+%2B+1+
(1) +u+=+2%2A1+%2B+1+
(1) +u+=+3+
---------------
The original number is 13
---------------
check:
(2) +10u+%2B+t+=+3%2A%28+10t+%2B+u+%29+-+8+
(2) +10%2A3+%2B+1+=+3%2A%28+10%2A1+%2B+3+%29+-+8+
(2) +31+=+3%2A13+-+8+
(2) +31+=+39+-+8+
(2) +31+=+31+
OK