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Common Core Standard HSA-CED.A.3 Questions

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

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Grade 10 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6
The sum of 2 numbers is 48, and their difference is 24. What are the numbers?
  1. 40 and 8
  2. 32 and 16
  3. 36 and 12
  4. 24 and 24
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.
  1. x+y+z=22,   2x+2y+2z=20,   2x+y+z=20;   (x,y,z)=(6,5,3)
  2. 2x+y+2z=22,   x+2y+2z=20,   x+2y+z+20;   (x,y,z)=(5,6,3)
  3. 2x+2y+z=22,   x+y+2x=20,   x+3y+z=20;   (x,y,z)=(5,3,6)
  4. x+y+2z=22,   2x+z+2z=20,   x+2y+2z=20;   (x,y,z)=(3,6,5)
Grade 10 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6
If you pay $11 for 1 apple and 9 bananas and pay $7 for 3 apples and 1 banana, how much does an apple and a banana cost?
  1. Apple = $ -1 Banana = $2/3
  2. Apple = $2 Banana = $1
  3. Apple = $1 Banana = $4/9
  4. Apple = $1/2 Banana = $1/2
Grade 10 Systems of Equations CCSS: HSA-CED.A.3, HSA-REI.C.6
The manager of the White Hall Spartan Movie Theatre found that Saturday's sales were $3,675. He knew that a total of 650 tickets were sold Saturday. Adult tickets cost $7.50, and children's tickets cost $4.50. How many of each kind of ticket were sold?
  1. Children: 250 tickets; Adults: 400 tickets
  2. Children: 160 tickets; Adults: 490 tickets
  3. Children: 344 tickets; Adults: 306 tickets
  4. Children: 400 tickets; Adults: 250 tickets
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