Find two numbers whose sum is 27

Solution:

Let one number be x, then second number = 27 – x

$x \times(27-x)=182$

$\Rightarrow 27 x-x^{2}=182$

$\Rightarrow x^{2}-27 x+182=0$

$\Rightarrow x^{2}-14 x-13 x+182=0$

$\Rightarrow x(x-14)-13(x-14)=0$

$\Rightarrow(x-13)(x-14)=0$

$\Rightarrow x=13$ or 14

$\Rightarrow 27 x=14$ or 13

Hence, the two marbles are 13 and 14 .