Question Number 176980 by Ar Brandon last updated on 29/Sep/22
$$\left({xy}\right)_{\mathrm{7}} =\left({yx}\right)_{\mathrm{9}} \\ $$$${x}+{y}=? \\ $$
Answered by mr W last updated on 29/Sep/22
$$\mathrm{7}{x}+{y}=\mathrm{9}{y}+{x} \\ $$$$\mathrm{3}{x}=\mathrm{4}{y} \\ $$$$\Rightarrow{x}=\mathrm{4}{t},\:{y}=\mathrm{3}{t} \\ $$$${since}\:{x},{y}\leqslant\mathrm{6}\: \\ $$$$\Rightarrow{t}=\mathrm{1}\: \\ $$$$\Rightarrow{x}=\mathrm{4},\:{y}=\mathrm{3} \\ $$$$\Rightarrow{x}+{y}=\mathrm{7} \\ $$
Commented by Ar Brandon last updated on 29/Sep/22
Thank you Sir