SOLUTION: what number am i? my ones digit is twice hundreds digit. My thousands digit is one less than the hundreds digit. My tens digit is the sum of my thousands and hundreds digit

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Question 1038588: what number am i? my ones digit is twice hundreds digit. My thousands digit is one less than the hundreds digit. My tens digit is the sum of my thousands and hundreds digit
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +u+ = the ones digit
Let +t+ = the tens digit
Let +h+ = the hundreds digit
Let +m+ = the thousands digit
--------------------------------
(1) +u+=+2h+
(2) +m+=+h+-+1+
(3) +t+=+m+%2B+h+
---------------------
There are 3 equations but there are 4 unknowns,
so, some guessing may be needed to solve
Substitute (2) into (3)
(3) +t+=+h+-+1+%2B+h+
(3) +t+=+2h+-+1+
------------------------
I'll put the results in order all in
terms of +h+, the hundreds digit:
+u+=+2h+
+t+=+2h+-+1+
+h+=+h+
+m+=+h+-+1+
----------------------------------
+h+ must be +4+ or less, because +u+
would be +10+ if +h+ was +5+
----------------------------------------
Suppose +h+=+4+
+u+=+2%2A4+
+u+=+8+
+t+=+2%2A4+-+1+
+t+=+7+
and
+h+=+4+
+m+=+4+-+1+|
+m+=+3+
----------------
So the number is 3478
--------------------
Suppose +h+=+3+
+u+=+2%2A3+
+u+=+6+
+t+=+2%2A3+-+1+
+t+=+5+
and
+h+=+3+
+m+=+3+-+1+
+m+=+2+
--------------------
So the number is 2356
---------------------
Suppose +h+=+2+
+u+=+4+
+t+=+3+
+h+=+2+
+m+=+1+
-------------
So, the number is 1234
----------------------
+h+ can't be +1+ because that
would make the thousands digit +0+
You have 3 choices, then
3478
2356
1234