Răspuns:
- [tex]\boxed{\bf a=\dfrac{805}{195}}[/tex]
- [tex]\boxed{\bf b=\dfrac{1127}{195}}[/tex]
- [tex]\boxed{\bf c=\dfrac{1771}{195}}[/tex]
Explicație pas cu pas:
(^_^) Salutare!
[tex]\bf 5a+7b+11c=161[/tex]
[tex]\bf Fie~\{a,b,c\}~ d.p.~ \{5,7,11\}[/tex]
[tex]\bf \dfrac{a}{5} = \dfrac{b}{7} = \dfrac{c}{11}=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}{11}=k \implies c=11 \cdot k[/tex]
[tex]\text{\it Inlocuim noile valori ale lui a,b,c in suma si vom avea:}[/tex]
[tex]\bf 5\cdot 5k+7\cdot7k+11\cdot 11k=161[/tex]
[tex]\bf 25k+49k+ 121k =161[/tex]
[tex]\bf 195k =161 \implies \boxed{\bf k = \dfrac{161}{195}}[/tex]
[tex]\bf a = 5\cdot \dfrac{161}{195}\implies \boxed{\bf a=\dfrac{805}{195}}[/tex]
[tex]\bf b = 7\cdot \dfrac{161}{195} \implies \boxed{\bf b=\dfrac{1127}{195}}[/tex]
[tex]\bf c = 11 \cdot \dfrac{161}{195}\implies \boxed{\bf c=\dfrac{1771}{195}}[/tex]
[tex]\it Veificare:[/tex]
[tex]\it 5\cdot \dfrac{805}{195}+7\cdot\dfrac{1127}{195} + 11\cdot \dfrac{1771}{195} =[/tex]
[tex]\it \dfrac{4025}{195}+\dfrac{7889}{195} + \dfrac{19481}{195} =[/tex]
[tex]\it \dfrac{4025+7889+19481}{195}=\dfrac{31395}{195}^{(195}=161 ~(adevarat)[/tex]
PS: Daca esti pe telefon, te rog sa glisezi spre dreapta pentru a vedea rezolvarea completa
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