SOLUTION: Find a two digit integer that is increased by 1/5 of its value if its digit are reversed

Question 696128: Find a two digit integer that is increased by 1/5 of its value if its digit are reversed
Found 2 solutions by ptaylor, KMST:
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
10x+y=the integer
When we reverse the digits, we have:
10y+x, soooo
10y+x=10x+y+(1/5)*(10x+y)
10y+x=10x+y+2x+y/5
10y-(6/5)y=11x
(44/5)y=11x
x=((44/5)y)/11
x=(44/55)y or
x=(4/5)y
y=5; x=4 This is the only possibility for 2-digit integers
So the integer has to be 45
CK
54=45+(1/5)*45=54
Hope this helps---ptaylor
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= first (tens) digit
= second (ones) digit
The number looks like ab,
but its value is .

The number formed when the digits are reversed looks like ba,
and its value is , which is larger.
The reversal of the digits increases the value by 1/5 to
of the original value,
making the reverse number equal to times the original number.
So

First we simplify:
--> --> -->

Next we solve:
--> --> --> -->

Since and are integers,
for to be the multiple of indicated by ,
must be a multiple of .
Since is a digit and a multiple of , it can only be .
So --> --> ,
and the original two-digit number is .
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