Fie a-I nr.
b-II
c-III
d-IV
e-V, atunci [tex] \frac{a+b+c+d+e}{5} =162[/tex] si
[tex] \frac{a}{3} =\frac{b}{4} =\frac{c}{5}[/tex] si
[tex]\frac{c}{3}=\frac{d}{4}=\frac{3}{5}[/tex];
pe ultimele doua le inmultim cu 5 si respectiv 3 ⇔
[tex]\frac{a}{9} =\frac{b}{12} =\frac{c}{15}[/tex] si
[tex]\frac{c}{15} =\frac{d}{20} =\frac{e}{25}[/tex] si
[tex] \frac{a+b+c+d+e}{5} =162[/tex] ⇔
[tex] \frac{a}{9}=\frac{b}{12}=\frac{c}{15}=\frac{d}{20}=\frac{e}{25}==\frac{a+b+c+d+e}{81} [/tex]
si
[tex] \frac{a+b+c+d+e}{5} =162[/tex] (a+b+c+d+e=810) ⇔
[tex] \frac{a}{9}=\frac{b}{12}=\frac{c}{15}=\frac{d}{20}=\frac{e}{25}=10 [/tex]
⇔
a=9*10
b=12*10
c=15 *10
d=20 *10
e=25*10
