Question

Aflati 4 nr. a caror suma este 5, stiind ca sunt invers proportionale cu nr 1 supra 2 , 1 supra 3 , 0.4 si 0.2.
VA ROOG !

Answer 1

a+b+c+d = 5

a/2 = b/3 = 0,4c = 0,2 d

a/2 = b/3 = c/2,5 = d/5 = a+b+c+d / 12,5 = 5/ 12,5

a= 0,8   b= 1,2   c= 1 d= 2

Answer 2

a+b+c+d=5;
a·1/2=b·1/3=c·4/10=d·2/10=k
⇒a·1/2=k⇒a=k/1/2⇒a=k·2⇒a=2k;
⇒b·1/3=k⇒b=k/1/3⇒b=k·3⇒b=3k;
⇒c·4/10=k⇒c·2/5=k⇒c=k/2/5⇒c=k·5/2⇒c=5k/2;
⇒d·2/10=k⇒d·1/5=k⇒d=k/1/5⇒d=k·5⇒d=5k;
⇒2k+3k+5k/2+5k=5
⇒4k/2+6k/2+5k/2+10k/2=5
⇒[4k+6k+5k+10k]/2=5
⇒25k/2=5
⇒25k=2·5
⇒25k=10
⇒k=10/25
⇒k=2/5;
⇒a=2·2/5⇒a=4/5;
⇒b=3·2/5⇒b=6/5;
⇒c=[5·2/5]/2⇒c=10/5/2⇒c=10/5·1/2⇒c=10/10⇒c=1;
⇒d=5·2/5⇒d=10/5⇒d=2;