Question

In tinutul de nicaieri traiesc spiridusi si zane . Media inaltimii spiridusilor este 60cm , iar media inaltimii zanelor este 160cm si media inaltimii spiridusilor si a zanelor este 120cm.
Daca sunt 12 spiridusi ,aflati cate zane sunt .
Plz !!!!AM NEVOIE URGENT!!!!!

Answer 1

Voi nota cu $s_{1}, s_{2}, s_{3}... s_{12}$ inaltimile celor 12 spiridusi si cu $z_{1}, z_{2}, z_{3},..., x_{n}$ inaltimile celor n zane.

$\frac{ s_{1}+ s_{2}+...+ s_{12} }{12}=60=> s_{1}+ s_{2}+ ...+ s_{12}=720(cm).$

$\frac{ z_{1}+ z_{2} + ...+z_{n} }{n}=160=> z_{1}+ z_{2}+...+ z_{n}=160n(cm).$

$\frac{ s_{1}+ s_{2}+...+ s_{12}+ z_{1}+ z_{2}+ ... z_{n} }{12+n}=120 <=> \\ <=> \frac{720+160n}{12+n}=120 =>720+160n=120(12+n) <=> \\ <=>720+160n=1440+120n => 160n-120n=1440-720<=> \\ <=>40n=720 => n=18.$

Deci sunt 18 zane.