SOLUTION: In a three digit number digits at tens place is 0 and the digit at the hundreds place is thrice the digit in the units place. If the digit at the 100th and units place is interchan

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: In a three digit number digits at tens place is 0 and the digit at the hundreds place is thrice the digit in the units place. If the digit at the 100th and units place is interchan      Log On


   

Question 875536: In a three digit number digits at tens place is 0 and the digit at the hundreds place is thrice the digit in the units place. If the digit at the 100th and units place is interchanged then sum of original numbe and new number is 404. Find the number


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +u+ = the units digit
Let +t+ = the tens digit
Let +h+ = the hundreds digit
----------------------------
(1) +t+=+0+
(2) +h+=+3u+
(3) +%28+100h+%2B+10t+%2B+u+%29+%2B+%28+100u+%2B+10t+%2B+h+%29+=+404+
------------------------------------------------
Substitute (1) into (3)
(3) +%28+100h+%2B+0+%2B+u+%29+%2B+%28+100u+%2B+0+%2B+h+%29+=+404+
(3) +100h+%2B+h+%2B+100u+%2B+u+=+404+
(3) +101h+%2B+101u+=+404+
Divide both sides by +101+
(3) +h+%2B+u+=+4+
------------------
Substitute (2) into (3)
(3) +3u+%2B+u+=+4+
(3) +4u+=+4+
(3) +u+=+1+
--------------
And
(2) +h+=+3u+
(2) +h+=+3+
--------------
The number is 301
check answer:
+103+%2B+301+=+404+
OK