Question

Impartim nr.3600 in patru parti ,astfel încat daca la prima parte adăugăm 5, din a doua scădem 5,a treia o înmulțit cu 5 ,iar a patra o impartim la 5,rezultatele sunt egale.aflati cele patru parti ?

Answer 1

 

$\displaystyle\\\text{Cele patru parti inegale in care a fost impartit 3600 sunt:}\\\\{\bf a,~b,~c,~d }\\\\a+b+c+d=3600\\\\a+5=b-5=c\times5=\frac{d}{5}=x\\\\ a=x-5\\\\b=x+5\\\\c=\frac{x}{5}\\\\d=5x\\\\a+b+c+d=3600\\\\(x-5)+(x+5)+\frac{x}{5}+5x=3600\\\\x+x+5x-5+5+\frac{x}{5}=3600\\\\7x+\frac{x}{5}=3600\\\\\frac{35x}{5}+\frac{x}{5}=3600\\\\\frac{36x}{5}=3600\\\\36x=3600\times5\\\\x=\frac{3600\times5}{36}\\\\x=100\times5\\\\\boxed{\bf x=500}$

$\displaystyle\\a=x-5=500-5~~\implies~~\boxed{\bf a=495}\\\\b=x+5=500+5~~\implies~~\boxed{\bf b=505} \\\\c=\frac{x}{5}=\frac{500}{5}~~\implies~~\boxed{\bf c=100} \\\\d=5x=5\times 500~~\implies~~\boxed{\bf d=2500}\\\\\\\text{Verificare:}\\\\495+505+100+2500=3600$