Question

Dividindo o número 3800 em partes
inversamente proporcionais aos valores 6, 12 e 15,
obtemos:
a) 2000, 900 e 900.
b) 3000, 400 e 400.
c) 2000, 800 e 1000.
d) 2000, 1200, e 600.
e) 2000, 1000 e 800.

Answer 1

Explicação passo-a-passo:

x+y+z=3800

x=k/6

y=k/12

z=k/15

Substituindo :

k/6+k/12+k/15=3800

k.(1/6+1/12+1/15)=3800

mmc:

6,12,15/3

2,4,5/2

1,2,5/2

1,1,5/5

1,1,1/___|

mmc(6,12,15)=3.2.2.5=60

k.([10+5+4]/60)=3800

k.(19/60)=3800

19k=60.(3800)

19k=228.000

k=228.000/19

k=12000

_____

X=k/6=1200/6= 2000

y=k/12=12000/12= 1000

z=k/15=12000/15= 800

____

Alternativa "E"

______

Espero ter ajudado!

Answer 2

x/6 + x/12 + x/15 =3800 ==> *(60)mmc

10x + 5x + 4x = 60*3800

19x = 60*3800 ==> :(19)

x = 60*200

x= 12000

A= x/6= 12000/6= 2000

B=x/12=12000/12=1000

C=x/15=12000/15= 800

===> e) 2000, 1000 e 800 ✓