SOLUTION: 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 he

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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