Question

Daca in fiecare lada se pun cate 35kg de cartofi raman 600kg cartofi netransporato, iar daca in fiecare lada punem 55kg atunci reman 40 lazi goale. cate lazi si cate kg de cartofi sunt?

Answer 1

Fie: x -> cantitatea de cartofi ce trebuie transportata
y -> numarul de lazi disponibile
Enuntul problemei se transcrie astfel:
$\left \{ {{35*y=x-600} \atop {55*(y-40)=x}} \right.$
Introducand pe x din a doua ecuatie in prima ecuatie obtinem:
$35y=55(y-40)-600$⇔$35y=55y-55*40-600$⇔
$55y-35y=2200+600$⇔$20y=2800$⇒
$y= \frac{2800}{20}$⇒$y=140 \ de \ lazi$
$\left \{ {{x=55*(y-40)} \atop {y=140}} \right.$⇒
$x=55*(140-40)$⇔$x=55*100$⇒$x=5500 \ kg \ cartofi$