Question

1.Impartiti numarul 3804 in parti invers proportionale cu 0.(6); 0.75;0.8;0.8(3)
2.Numerele x si y sunt invers proportionale cu 6 si respectiv 5. Calculati valorile rapoartelor : 3x+8y/5x+y ; x la patrat+ y la patrat/ 8xy Va rog sa ma ajutati . Multumesc enorm!

Answer 1

1) 0,(6)=6/9=2/3;
0,75=3/4;
0,8=4/5;
0,8(3)=(83-8)/90=75/90=5/6;
a+b+c+d=3804;
2a/3=3b/4=4c/5=5d/6=k ⇒ a=3k/2, b=4k/3, c=5k/4, d=6k/5;
3k/2+4k/3+5k/4+6k/5=(90k+80k+75k+72k)/60=317k/60=3804 ⇒ k=720 ⇔ 
a=1080, b=960, c=900, d=864.
2) 6x=5y ⇒ x/y=5/6 ⇒ 3x/y=15/6 ⇒ 3x/8y=15/48=5/16 ⇒ (3x+8y)/8y=21/16 ⇒ 
(3x+8y)/y=21/2;
x/y=5/6 ⇒ 5x/y=25/6 ⇒ (5x+y)/y=31/6;
(3x+8y)/(5x+y)=21/2:31/6=63/31;