let
mass of each rock = x
mass of each mineral = y
Therefore,
[tex]\begin{gathered} 4x+7y=120 \\ 5x+2y=69 \\ \\ 7y=120-4x \\ y=\frac{120}{7}-\frac{4x}{7} \\ 5x+2(\frac{120}{7}-\frac{4x}{7})=69 \\ 5x+\frac{240}{7}-\frac{8x}{7}=69 \\ 5x-\frac{8x}{7}=69-\frac{240}{7} \\ \frac{35x-8x}{7}=\frac{483-240}{7} \\ \frac{27x}{7}=\frac{243}{7} \\ \text{cross multiply} \\ 189x=1701 \\ x=\frac{1701}{189} \\ x=9 \\ \\ 4x+7y=120 \\ 4(9)+7y=120_{} \\ 7y=120-36 \\ 7y=84 \\ y=\frac{84}{7} \\ y=12 \end{gathered}[/tex]Mass of a rock = 9 grams
Mass of a Mineral = 12 grams
