Question

Intr-o ferma este un numar de animale. Jumatate din ele sunt pasari : gaini , rate si gaste , 1 supra 3 din rest sunt ovine , 1 supra 2 din noul rest sunt vaci , 2 supra 3 din noul rest sunt vitei si 164 de cai. Cate gaini , rate si gaste sunt , stiind ca numarul lor reprezinta suma a trei numere pare consecutive?

Answer 1

x=nr animale
x/2=pasari
x-x/2=x/2=rest
x/2×1/3=x/6=ovine
x/2-x/6=x/3=rest
x/3×1/2=x/6=vaci
x/3-x/6=x/6=rest
x/6×2/3=x/9=vitei
x/2+x/6+x/6+x/9+164=x
x/2+x/3+x/9+164=x
9x+6x+2x+2952=18x
x=2952 animale
x/2=2952/2=1476 pasari
x/6=1476/6=246 ovine
x/6=1476/6=246 vaci
x/9=1476/9=164 vitei

1476 pasari
2a+2a+2+2a+4=1476
6a=1470
a=245
245x2=490 gaini
490+2=492 rate
492+2=494 gaste