Răspuns:
- [tex]\boxed{\bf a=150}[/tex]
- [tex]\boxed{\bf b=210}[/tex]
- [tex]\boxed{\bf c=240}[/tex]
Explicație pas cu pas:
(*^_^*) Salutare!
[tex]\bf a+b+c=600[/tex]
[tex]\bf Fie~\{a,b,c\}~ d.p.~ \{5,7,8\}[/tex]
[tex]\bf \dfrac{a}{5} = \dfrac{b}{7} = \dfrac{c}{8}=k \implies[/tex]
[tex]\text{\it Notam valoarea comun a acestor rapoarte cu k (coeficient de proportionalitate)}[/tex]
[tex]\bf \dfrac{a}{5} =k \implies\bf a=5\cdot k[/tex]
[tex]\bf \dfrac{b}{7} =k \implies b=7\cdot k[/tex]
[tex]\bf \dfrac{c}{8}=k \implies c=8\cdot k[/tex]
[tex]\text{\it Inlocuim noile valori ale lui a,b,c in suma si vom avea:}[/tex]
[tex]\bf 5k+7k+8k=20k[/tex]
[tex]\bf 20k=600~~\bigg|:20[/tex]
[tex]\boxed{\bf k=30}[/tex]
[tex]\bf a = 5\cdot 30\implies \boxed{\bf a=150}[/tex]
[tex]\bf b = 7\cdot 30\implies \boxed{\bf b=210}[/tex]
[tex]\bf b = 8\cdot 30\implies \boxed{\bf c=240}[/tex]
[tex]\it Veificare:[/tex]
[tex]\it 150+210+240 = 600~(adevarat)[/tex]
==pav38==
