SOLUTION: In a 2-digit number, the number in the units place is 4 more then the number in the tens place. if the digits or the number are reversed, the new number is 6 more than thrice the o

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: In a 2-digit number, the number in the units place is 4 more then the number in the tens place. if the digits or the number are reversed, the new number is 6 more than thrice the o      Log On


   

Question 908633: In a 2-digit number, the number in the units place is 4 more then the number in the tens place. if the digits or the number are reversed, the new number is 6 more than thrice the original number. whats the original number
Found 2 solutions by ewatrrr, josmiceli:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x the ten's digit, (x+4) unit's digit
Write as You read and Solve
if digits of the number are reversed...
10(x+4) + x = 3(10x + (x+4)) + 6
10(x+4) + x = 3(11x+4)) + 6
11x + 40 = 33x + 18
22 = 22x
1 = x
Number is: 15
checking..........
51 = 45 + 6

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the units digit = +u+
Let the tens digit = +t+
The "value" of the number is:
+10t+%2B+u+
The value with the digits reversed is:
+10u+%2B+t+
--------------------------
(1) +u+=+t+%2B+4+
(2) +10u+%2B+t+=+3%2A%2810t+%2B+u%29+%2B+6+
---------------------------
(2) +10u+%2B+t+=+30t+%2B+3u+%2B+6+
(2) +10u+-+3u+-+30t+%2B+t+=+6+
(2) +7u+-+29t+=+6+
---------------------
Substitute (1) into (2)
(2) +7%2A%28+t+%2B+4+%29+-+29t+=+6+
(2) +7t+%2B+28+-+29t+=+6+
(2) +22t+=+22+
(2) +t+=+1+
and
(1) +u+=+t+%2B+4+
(1) +u+=+1+%2B+4+
(1) +u+=+5+
-----------------
The original number is +15+
check:
Reverse the digits: +51+
---------------------
+51+=+3%2A15+%2B+6+
+51+=+45+%2B+6+
+51+=+51+
OK