Question

Aflați a+b+c știind ca abc+bca+cab=1443​

Answer 1

 

$\displaystyle\bf\\Se~stie~ca:\\\\\overline{abc}+\overline{bca}+\overline{cab}=1443\\\\Se~cere:\\\\a+b+c=~?\\\\Rezolvare:\\\\\overline{abc}+\overline{bca}+\overline{cab}=1443\\\\(100a+10b+c)+(100b+10c+a)+(100c+10a+b)=1443\\\\Grupam:\\100a+10a+a+100b+10b+b+100c+10c+c=1443\\\\a(100+10+1)+b(100+10+1)+c(100+10+1)=1443\\\\111a+111a+111a=1443\\\\111(a+b+c)=1443\\\\a+b+c=\frac{1443}{111}\\\\\boxed{\bf~a+b+c=13}$