SOLUTION: Can you please assist me in the following: A number is ten times the sum of its digits. The tens digit is two greater than the units digit. Find the number. so far I only manage

Question 174778: Can you please assist me in the following: A number is ten times the sum of its digits. The tens digit is two greater than the units digit. Find the number.
so far I only managed to write:
10n=n+m
m=2+10n
10n=n+(2+10n)
10n=n+2+10n
10n=11n+2
n=-2
10(-2)=(-2)+m
-20=-2+m
m=-18
10(-2)=(-2)+(-18)
(-18)=2+10(-2)
-20=-20
-18=-18
would this be the correct answer
Found 3 solutions by stanbon, checkley75, josmiceli:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Can you please assist me in the following: A number is ten times the sum of its digits. The tens digit is two greater than the units digit. Find the number.
-------------------------
Usually these problems involve a two-digit number. You have only two equation
statements so I'm going to assume the number is 2-digit.
------------------------
Let the number be 10t+u where t is the tens and u is the units digit.
-------------
Equations:
10t+u = 10(t+u)
t = u + 2
---------------
Rearrange:
10t+u = 10t+10u
9u = 0
u = 0
-----------
Since t = u+2, t = 0+2 = 2
-------------
The number is 20
=====================
Cheers,
Stan H.
Answer by checkley75(3666)   (Show Source): You can put this solution on YOUR website!
10x+y=10(x+y)
x=y+2
10(y+2)+y=10(y+2+y)
10y+20+y=10(2y+2)
11y+20=20y+20
11y-20y=0
y=0 ans. for the units integer.
x=0+2
x=2 for the tens integer
Proof:
10*2+0=10(2+0)
20+0=20
20=20

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
The number is
(1) First of all, if a number is times anything,
The units digit must be
(2) The problem says the tens digit is two greater
that the units digit, so the tens digit must be
This satisfies the problem
For any number greater than 20, either (1) or (2) is violated,
or ten times the sum of the digits will always be less than
the number itself
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