Math
posted by Raihan .
Determine all pairs (m, n) of a twodigit natural number m and a singledigit natural number n satisfying the following conditions.
1) If the number n is given as the number between the two digits of the number m, then a threedigit number is obtained which is 11 times the number m.
2) If the number n is used as a number before the decimal number of the number m, then a threedigit number is obtained that is 21 times as large as the number n.

If I understand this correctly, then if the digits of m are a and b, we have
m = 10a+b
and so
100a+10n+b = 11(10a+b)
100n+10a+b = 21n
But this comes out with negative solutions. Maybe you can fix my logic and take it where it's supposed to go.
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