Question

Aflati trei numere rationale ce sunt invers proportionale cu 0,(3); 0,25; 0,2 si au media aritmetica egala cu 60. * rezultate ( de la sfarsitul cartii ) : 45, 60, 75 *.

Answer 1

x3/9=y25/100=z2/10      x1/3=y1/4=z1/5 =k        x=3k     y=4k          z=5k        x+y+z=180       3k+4k+5k=180       12k=180    k=5     x=15     y=20       z=25

Answer 2

0,(3)=3/9 simplificam=1/3
0,25=25/100 simplificam=1/4
0,2=2/10 simplificam=1/5
60=a+b+c/3
{a,b,c,} i.p.{1/3, 1/4, 1/5
a/3=b/4=c/5=k
a/3==k⇒a=3k
b/4=k⇒b=4k
c/8=k⇒c=5k
60=(3k+4k+5k)/3
12k=60·3
k=180/12
k=15
a=3k=3·15=45
b=4k=4·15=60
c=5k=5·15=75