Question

suma a 3 numere este 130 . stiinfd ca ele sunt invers proportionale cu 2,3,4 .
aflati numerele .

Answer 1

a+b+c=130
2a=3b=4c=k
a=k:2
b=k:3
c=k:4
k:2+k:3+k:4=130
6k+4k+3k=1560
13k=1560
k=120
a=60 b=40 c=30

Answer 2

{ a, b, c } i.p { 2, 3, 4 }
a x 2 = b x 3 = c x 4 = k
a x 2 = k ⇒ a = k/2
b x 3 = k ⇒ b = k/3
c x 4 = k ⇒ c = k/2
a + b + c = 130
k/2 + k/3 + k/4 = 130 ( numitorul comun  e 12 )
6k/12 + 4k/12 + 3k/12 = 130
13k/12 = 130
13k = 130 x 12
13k = 1560
k = 120
a = 120/2 = 60
b = 120/3 = 40
c = 120/4 = 30