Question

sa se imparta numarul 555 in larti invers proportionale cu numerele 5,6 si 4

Answer 1

Consideram partile a,b,c. Daca numarul 555 se imparte in parti invers proportionale cu 5,6,4, atunci partile adunate este a+b+c=555.
{a,b,c} ip {5,6,4}
a=k/5
b=k/6
c=k/4
k/5+k/6+k/4=555
12k/60+10k/60+15k/60=555
(12k+10k+15k)/60=555
37k/60=555
37k=555*60
37k=33300
k=33300/37
k=900

a=k/5=900/5=180
b=k/6=900/6=150
c=k/4=900/4=225
Verificare:
a+b+c=555
180+150+225=555
555=555
Solutia este buna.

Answer 2

{a, b, c} i. p {5,6,4}
a×5=b×6=c×4 =k
a= k/5
b=k/6
c=k/4
a+b+c=555
k/5+k/6+k/4=555
12k+10k +15k/60=555
37k/60=555
k= 555:37/60
k= 555×60/37
k=900
a=k/5=900/5=180
b=k/6=900/6=150
c=k/4=900/4=225

Verificare : 180+150+225= 555