Systems of Equations Question
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Grade 11 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6
Kevin weighs sets of small rock samples for his science class. A set of 2 quartz, 2 mica, and 1 granite rocks weigh 22 grams. A set of 1 quartz, 1 mica, and 2 granite rocks weigh 20 grams. A set of 1 quartz, 3 mica, and 1 granite rocks weigh 20 grams. Samples of each rock type have the same weight. Write a system of linear equations. Solve the system to determine the weight of each rock. x = weight on the quartz rock, y = the weight of the mica rock, and z = the weight of the granite rock.
- x+y+z=22, 2x+2y+2z=20, 2x+y+z=20; (x,y,z)=(6,5,3)
- 2x+y+2z=22, x+2y+2z=20, x+2y+z+20; (x,y,z)=(5,6,3)
- 2x+2y+z=22, x+y+2x=20, x+3y+z=20; (x,y,z)=(5,3,6)
- x+y+2z=22, 2x+z+2z=20, x+2y+2z=20; (x,y,z)=(3,6,5)