Question

Mr. Pichola's science class is doing a project involving rocks and minerals. Justin found the mass of 4 rocks and 7minerals to be 120 grams. Brittany found the mass of 5 rocks and 2 minerals to be 69 grams. What is the massof a rock? What is the mass of a mineral?

Answer 1

let

mass of each rock = x

mass of each mineral = y

Therefore,

`\begin{gathered} 4x+7y=120 \\ 5x+2y=69 \\ \\ 7y=120-4x \\ y=(120)/(7)-(4x)/(7) \\ 5x+2((120)/(7)-(4x)/(7))=69 \\ 5x+(240)/(7)-(8x)/(7)=69 \\ 5x-(8x)/(7)=69-(240)/(7) \\ (35x-8x)/(7)=(483-240)/(7) \\ (27x)/(7)=(243)/(7) \\ \text{cross multiply} \\ 189x=1701 \\ x=(1701)/(189) \\ x=9 \\ \\ 4x+7y=120 \\ 4(9)+7y=120_{} \\ 7y=120-36 \\ 7y=84 \\ y=(84)/(7) \\ y=12 \end{gathered}`

Mass of a rock = 9 grams

Mass of a Mineral = 12 grams