Digit sum

The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?

Correct result:

c₁ =  45
c₂ =  54

Solution:

$$\begin{gathered} c=10x+y \\ x+y=9 \\ c\cdot (10y+x)=2430 \\ c:18,27,36,45\dots \\ {v}_1=18\cdot 81=1458 \\ {v}_2=27\cdot 72=1944 \\ {v}_3=36\cdot 63=2268 \\ {v}_4=45\cdot 54=2430 \\ {c}_1=45 \end{gathered}$$

$c_2=54$

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