Question

Fie x,y apartine Nr naturale prime intre ele.Aflati valoarea raportului x/y stiind proportiile:
a) x-y/y=3/4
b) 2x+y/y=73/15
 c)3x-y/2y = 9/4
d) x+y/x-y = 7/3

Answer 1

a) (x-y)/y=3/4 ⇒ (x-y+y)/y=(3+4)/3 ⇒ x/y=7/3;
b) (2x+y)/y=73/15 ⇒ (2x+y-y)/y=(73-15)/15 ⇒ 2x/y=58/15 ⇒ x/y=29/15;
c) (3x-y)/2y=9/4 ⇒ (3x-y)/y=9/2 ⇒ (3x-y+y)/y=(9+2)/2 ⇒ 3x/y=11/2 ⇒ x/y=11/6;
d) (x+y)/(x-y)=7/3 ⇒ (x+y+x-y)/(x-y)=(7+3)/3 ⇒ 2x/(x-y)=10/3 ⇒ x/(x-y)=5/3 ⇒ 
x/(x-y-x)=5/(3-5) ⇒ x/-y=5/-2 ⇒ x/y=5/2.