Question

Numerelea si b sunt invers proportionale cu 2,3.daca 6a+9b=36 atunci determinati numerele a si b

Answer 1

a. a·2=b·3=k;
⇒a·2=k⇒a=k/2;
⇒b·3=k⇒b=k/3;
⇒6a+9b=36⇒6k/2+9k/3=36⇒3k+3k=36⇒6k=36⇒k=36;
⇒a=36/2⇒a=18;
⇒b=36/3⇒b=12;
b. a·2=b·3=c·4=k;
⇒a·2=k⇒a=k/2;
⇒b·3=k⇒b=k/3;
⇒c·4=k⇒c=k/4;
⇒6a+9b-4c=75⇒6k/2+9k/3+4k/4=75⇒3k+3k-1k=75⇒6k-1k=75⇒5k=75⇒k=15;
⇒a=15/2⇒a=7,5;
⇒b=15/3⇒b=5;
⇒c=15/4⇒c=3,75;