Question

Numerele a,b,c sunt direct proportionale cu 4,5si 8 si 2a+3b+5c=630.Aflati a,b,c.

Answer 1

{ a,b,c } d.p { 4,5,8 } 
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2a + 3b + 5c = 630
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a / 4 = b / 5 = c / 8 = K

a / 4 =  K = > a = 4 K
b / 5 = K = > b = 5 K
c /  8 = K = > c  = 8 K

2 x 4 K + 3 x 5 K + 5 x 8 K  = 630
8 K + 15 K + 40 K = 630
23 K  + 40 K = 630
63 K = 630
K = 630 : 63
K  = 10

a = 10 x 4 = 40

b = 10 x 5 = 50

c = 10 x 8  = 80

Answer 2

{a,b,c} d.p.{4,5,9}
a/4=b/5=c/8=k ⇒ a=4k ; b=5k ; c=8k
2a+3b+5c=630
2×4k+3×5k+5×8k=630 ⇒8k+15k+40k=630⇒ 63k=630⇒ k=10
a=4k=4×10=40 ; b=5k=5×10=50 ; c=8k=8×10=80
a = 40;  b = 50  si c= 80

verificare
2a+3b+5c=630
2×40+3×50+5×80=
80+150+400=630
630=630