Question

aflati numerele a,b,c stiind ca acestea sunt direct proportionale cu 5,7 si 8 si a+b+c=600
repede dau coroana

Answer 1

{a,b,c} d.p. {5,7,8}

$\frac{a}{5}=\frac{b}{7} = \frac{c}{8}$ ⇒ a=5k, b=7k, c=8k

5k+7k+8k=20k

$=>_{ipoteza}$ 20k=600

=> k=600÷20

=> k=30

Daca k=30 =>

a= 5k= 30×5=150

b=7k=30×7=210

c=8k=30×8=240

Verificam : 150+210+240=600

Bafta!

Answer 2

Răspuns:

• $\boxed{\bf a=150}$
• $\boxed{\bf b=210}$
• $\boxed{\bf c=240}$

Explicație pas cu pas:

(*^_^*) Salutare!

$\bf a+b+c=600$

$\bf Fie~\{a,b,c\}~ d.p.~ \{5,7,8\}$

$\bf \dfrac{a}{5} = \dfrac{b}{7} = \dfrac{c}{8}=k \implies$

$\text{\it Notam valoarea comun a acestor rapoarte cu k (coeficient de proportionalitate)}$

$\bf \dfrac{a}{5} =k \implies\bf a=5\cdot k$

$\bf \dfrac{b}{7} =k \implies b=7\cdot k$

$\bf \dfrac{c}{8}=k \implies c=8\cdot k$

$\text{\it Inlocuim noile valori ale lui a,b,c in suma si vom avea:}$

$\bf 5k+7k+8k=20k$

$\bf 20k=600~~\bigg|:20$

$\boxed{\bf k=30}$

$\bf a = 5\cdot 30\implies \boxed{\bf a=150}$

$\bf b = 7\cdot 30\implies \boxed{\bf b=210}$

$\bf b = 8\cdot 30\implies \boxed{\bf c=240}$

$\it Veificare:$

$\it 150+210+240 = 600~(adevarat)$

==pav38==