x - ilość solanki 10%

y - ilość solanki 4% 

$\{\begin{array}{l}x+y=15\\ 10\%\cdot x+4\%\cdot y=6\%\cdot 15\end{array}$  

$\{\begin{array}{l}x+y=15\mid -x\\ 0.1x+0.04y=0.06\cdot 15\mid \cdot 100\end{array}$ $\{\begin{array}{l}x+y=15\mid -x\\ 0.1x+0.04y=0.06\cdot 15\mid \cdot 100\end{array}$  

$\{\begin{array}{l}y=15-x\\ 10x+4y=90\end{array}$  

$\{\begin{array}{l}y=15-x\\ 10x+4\left(15-x\right)=90\end{array}$  

$\{\begin{array}{l}y=15-x\\ 10x+60-4x=90\mid -60\end{array}$  

$\{\begin{array}{l}y=15-x\\ 6x=30\mid :6\end{array}$  

$\{\begin{array}{l}y=15-x\\ x=5\end{array}$  

$\{\begin{array}{l}y=15-5=10\\ x=5\end{array}$  

Odpowiedź:

Należy wziąć 5 kg solanki 10% i 10 kg solanki 4%.