Question 126252: I'm stumped and need help with this Algebra problem...
Find 2 numbers that are 13 times the sum of their digits
I tried this but it does not seem to work out... can you help?
xy = 13(x+y)
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
Let  be the two integer that are respectively 13 times
the sum of its digits.
Note that  be  number (the digits are from 0-9, and 9*13=117).
Let 
Then 
We can show that M cannot be a number.
If M is the number  number  and all digits are  , then
 ….=>… not possible
Similarly, larger numbers are not possible.
We can also show that  cannot be a  number and both digits are .
If is the number , then
 ….
=>…  …
.=>…  …
.=>…  ….=>…
.=>… possible since  and 
So the answers can only be  numbers. Let be  , then
 ……………..divide by 
If  , the equation becomes  . We have the following sets of solutions:
 |  | 
 | | 
|  | 
|  |
If  , the equation becomes  . This has no solution as the largest value of  is  (when  and
 ).
Similarly, there is no solution for 
Therefore, the possible values of are  ,  and  .
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