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:

$c=10x+y \ \\ x+y=9 \ \\ c \cdot \ (10y+x)=2430 \ \\ c: 18, 27, 36, 45 ... \ \\ v_{1}=18 \cdot \ 81=1458 \ \\ v_{2}=27 \cdot \ 72=1944 \ \\ v_{3}=36 \cdot \ 63=2268 \ \\ v_{4}=45 \cdot \ 54=2430 \ \\ c_{1}=45$

$c_{2}=54$

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