SOLUTION: The sum of the digits of a two-digit number is 13. When the digits are reversed, the new number is 27 more than the original number. What is the original number? (The worksheet

Question 480647: The sum of the digits of a two-digit number is 13. When the digits are reversed, the new number is 27 more than the original number. What is the original number?
(The worksheet says at the top "Applying Systems")
Found 2 solutions by Anthea Lawn, emargo19:
Answer by Anthea Lawn(22) (Show Source): You can put this solution on YOUR website!
Lets say the 2 digit number is xy
That is to say the "tens" digit is x and the "units" digit is y (ie. by xy we don't mean x times y)
So the value of the original number is 10x + y (because the x is in the "tens" column, just like 35 is 3 times 10 plus 5 for example)
If you reverse the digits then the value of the new number is 10y + x
.. and we know that this number is 27 more than the original .. so ...
(10y + x) = (10x + y) + 27
Take an x away from each side
10y = 9x + y + 27
Take a y away from each side
9y = 9x + 27
.. and we can divide both sides by 9 to make it a bit simpler
y = x + 3
So we are looking for a 2 digit number in which one digit is 3 more than the other.
We are also told that the sum of the digits is 13
x + y = 13
Since we know that y = x + 3 (from above) we can substitute for y
x + (x + 3) = 13
So x = 5 which means that y = 8
Therefore the original number was 58, which when reversed becomes 85
Answer by emargo19(101) (Show Source): You can put this solution on YOUR website!
Let one be n
Let tens=t
----eq1
-----eq2

Lets sorts the terms in eq2

multiply eq1 by (9)

---------------

substitute n=8 in eq1
So,

and
The original number is

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