Question

Calculati numerele x,y si z invers proportionale cu numerele 6,8 si 15 , stiind ca suma lor este egala cu 473. VA ROOG SCRIETI SI REZOLVAREA!!!

Answer 1

x·6=y·8=z·15=k
⇒x·6=k⇒x=k/6;
⇒y·8=k⇒y=k/8;
⇒z·15=k⇒z=k/15;
x+y+z=473
⇒k/6+k/8+k/15=473
⇒20k/120+15k/120+8k/120=473
⇒[20k+15k+8k]/120=473
⇒43k/120=473
⇒43k=473·120
⇒43k=56760
⇒k=56760/43
⇒k=1320;
⇒x=k/6
⇒x=1320/6⇒x=220;
⇒y=1320/8⇒y=165;
⇒z=1320/15⇒z=88;