Question

Simona pune ciresele pe care le-a cules in ladite.Daca pune cate 7 kg ,nu incape 1 kg.Daca pune cate 9 kg ,raman 12 ladite goale si o ladota cu 8 kg.Cate kg de cirese si ladite are Simona?

Answer 1

[tex]\displaystyle\\
x=\text{cantitatea de cirese}\\
y=\text{numarul de lazi}\\
\begin{cases}
x=7y+1\\
y=\dfrac{x-8}{9}+12+1~~~\Big|\cdot 9
\end{cases} \\\\
\begin{cases}
x-7y=1\\
9y=x-8+9\cdot 13
\end{cases} \\\\
\begin{cases}
x-7y=1\\
-x+9y=-8+117
\end{cases} \\\\
\begin{cases}
x-7y=1\\
-x+9y=109
\end{cases} \\\\
\text{Adunam ecuatiile.}\\
2y=110\\
y=\frac{110}{2}=\boxed{55 \text{ de lazi}}\\
x=7y+1=7\cdot 55+1=\boxed{386 \text{ Kg de cirese}}[\tex]