Question Number 161282 by byaw last updated on 15/Dec/21
Answered by alephzero last updated on 16/Dec/21
$$\boldsymbol{{First}}\:\boldsymbol{{method}}. \\ $$$$\frac{{u}}{\mathrm{2}}\:\rightarrow\:{u}\:\rightarrow\:\mathrm{3}.\mathrm{14}{u} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{3}\:\rightarrow\:\mathrm{6}\:\rightarrow\:\mathrm{3}.\mathrm{14}{u}\:=\:? \\ $$$${u}\:=\:\mathrm{6}\:\Rightarrow\:\mathrm{3}.\mathrm{14}\left(\mathrm{6}\right)\:=\:\mathrm{18}.\mathrm{84}\: \\ $$$$\left(\mathrm{2}\right)\:\frac{{u}}{\mathrm{2}}\:\rightarrow\:\mathrm{10}\:\rightarrow\:\mathrm{50}.\mathrm{24} \\ $$$${u}\:=\:\mathrm{10}\:\Rightarrow\:\frac{{u}}{\mathrm{2}}\:=\:\frac{\mathrm{10}}{\mathrm{2}}\:=\:\mathrm{5} \\ $$$${Answer}:\:{x}\:=\:\mathrm{18}.\mathrm{84},\:{y}\:=\:\mathrm{5} \\ $$$$\boldsymbol{{Second}}\:\boldsymbol{{method}}. \\ $$$${k}\:\rightarrow\:\mathrm{2}{k}\:\rightarrow\:\mathrm{3}.\mathrm{14}×\mathrm{2}{k} \\ $$$$\mathrm{3}.\mathrm{14}×\mathrm{2}\:=\:\mathrm{6}.\mathrm{28} \\ $$$$\Rightarrow\:{k}\:\rightarrow\:\mathrm{2}{k}\:\rightarrow\:\mathrm{6}.\mathrm{28}{k} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{3}\:\rightarrow\:\mathrm{6}\:\rightarrow\:\mathrm{6}.\mathrm{28}{k} \\ $$$${k}\:=\:\mathrm{3}\:\Rightarrow\:\mathrm{6}.\mathrm{28}{k}\:=\:\mathrm{6}.\mathrm{28}×\mathrm{3}\:=\:\mathrm{18}.\mathrm{84} \\ $$$$\left(\mathrm{2}\right)\:{k}\:\rightarrow\:\mathrm{10}\:\rightarrow\:\mathrm{50}.\mathrm{24} \\ $$$$\mathrm{2}{k}\:=\:\mathrm{10}\:\Rightarrow\:{k}\:=\:\frac{\mathrm{10}}{\mathrm{2}}\:=\:\mathrm{5} \\ $$$${Answer}:\:{x}\:=\:\mathrm{18}.\mathrm{84},\:{y}\:=\:\mathrm{5} \\ $$
Commented by MJS_new last updated on 16/Dec/21
$$\mathrm{but}\:\mathrm{in}\:\mathrm{the}\:\mathrm{last}\:\mathrm{line}\:\frac{{u}}{\mathrm{2}}\:\rightarrow\:{u}\:\rightarrow\:\mathrm{3}.\mathrm{14}{u}\:\mathrm{doesn}'\mathrm{t} \\ $$$$\mathrm{work}\:\mathrm{because}\:\mathrm{3}.\mathrm{14}×\mathrm{5}\neq\mathrm{50}.\mathrm{24} \\ $$
Commented by alephzero last updated on 16/Dec/21
$${Hm}…\:{You}'{re}\:{right}! \\ $$