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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 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. [math]x + y + z = 22, \ \ \ 2x + 2y + 2z = 20, \ \ \ 2x + y + z = 20; \ \ \ (x,y,z) = (6, 5,3)[/math]
  2. [math]2x+y+2z=22, \ \ \ x+2y+2z=20, \ \ \ x+2y+z+20; \ \ \ (x,y,z) = (5,6,3)[/math]
  3. [math]2x+2y+z=22, \ \ \ x+y+2x=20, \ \ \ x+3y+z=20; \ \ \ (x,y,z) = (5,3,6)[/math]
  4. [math]x+y+2z=22, \ \ \ 2x+z+2z=20, \ \ \ x+2y+2z=20; \ \ \ (x,y,z) = (3,6,5)[/math]
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
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
Alyssa has $2.70 in change in her purse. Her coins consist only of dimes and nickels. She has 39 total coins. How many dimes and nickels does she have?
  1. 14 dimes, 25 nickels
  2. 15 dimes, 24 nickels
  3. 13 dimes, 26 nickels
  4. 12 dimes, 27 nickels
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