Writing Systems with 3 Variables

There are 15 animals in a barn.  These animals are horses and chickens and cows.  There are 44 legs in all.  There are 4 times as many chickens than there are horses. If horses are represented by x, chickens are represented by y, and cows are represented by z, then which system of equations represents the situation?

• x + y + z = 15
  4x + 2y + 4z = 44

  4x = y

• 4x + 2y + 4z = 15
  x + y + z = 44

  4y = x

• x + z = 2y + 44
  4x - 4z = y + 15

  4 + x = y

• 2x - 4y - 4z = 44
  x - y - z = 15

  4 + y = x

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas and a watermelon for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. On Friday she purchased 2 apples and 8 bananas and 1 watermelon for $15. Which system of equations represents the situation?

• 4x + 6y = 3 + z

  13.5x - 13y - z= 6

  8x + 2y + z = 15

• x + y + z = 4

  x - y - z = 6

  8x + 2y - z = 15

• 4x + 6y + z = 13

  3x + 7y = 13.5

  2x + 8y + z = 15

• 4x - 6y - z = 13

  3x - 7y = 13.5

  2x + 8y - z = 15

Tags

CCSS.HSA.CED.A.3

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740 and they sold twice as many student tickets than adult tickets, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740

  2A = S

• S + A = 530
  4S + 3A = 1740

  2A = S

• S + A = 1740
  3S + 4A = 530

  2S = A

• S + A = 1740
  4S + 3A = 530

  2S = A

Tags

CCSS.HSA.CED.A.3

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills and ten dollar bills. She has 6 more twenty dollar bills than she does fifty dollar bills. Which system best represents the situation?

• x + y + z = 1430

  20x + 50y + 10z = 49

  x + 6 = y

• x + y + z = 49

  10x + 5y + 20z = 1430

  x + 6 = y

• x + y + z = 49

  20x + 50y + 10z = 1430

  y + 6 = x

• x + y +z = 49

  x + y - z = 1430

  y + 6 = x - z

Tags

CCSS.HSA.CED.A.3

The cost of 5 squash and 2 zucchini and 3 avocado is $1.32. Three squash and 1 zucchini and 2 avocados cost $0.75. Eight squash and 4 zucchini costs $1. 92. Write a system of equations for the cost of a squash, q, and cost of zucchini, z.

• 5q + 2z - 3a = 1.32
  1z - 2a = 0.75

  4q + 8z = 1.92

• 5q + 2z + 3a = 1.32
  3q + 1z + 2a = 0.75

  8q + 4z = 1.92

• q + z + a = 1.32
  q + z - a = 0.75

  8q + 4z = 1.92

• 5q + 2z + 3a = 0.75
  3q + 1z + 2a = 1.32

  4q + 8z = 1.92

Tags

CCSS.HSA.CED.A.3

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

• x+y=134
  x+y=120
• 3x+3y=134
  4x+3y=120
• 4x+3y=134
  3x+3y=120
• 7xy=134
  6xy=120

Tags

CCSS.HSA.CED.A.3

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

• 3H + 2D = 315

  2H + 4D = 450

• 3H + 2D = 450

  2H + 4D = 315

• 2H + 4D = 315

  3H + 2D = 450

• 3H + 2D = 315

  2H + 2D = 135

Tags

CCSS.8.EE.C.8C

David is running a concession stand at a soccer game. He sells nachos and sodas and soft pretzels. Nachos cost $1.50 each and sodas cost $0.50 each and soft pretzels cost $2. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas and pretzels combined. David sold 25 less nachos than sodas. Which system of equations represents this situation?

• 1.5N + 0.5S + 2P = 78.5

  N + S + P = 87

  S - 25 = N

• 1.5N + 0.5S + 2P = 78.5

  1.5N + 0.5S - 2P = 87

  S - 25 = N

• N + S + P = 78.5

  1.5N + 0.5S + 2P = 87

  N - 25 = S

• N + S + P= 78.5

  N + S - P = 87

  N - 25 = S

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child ticket

• 3S+C=38

  3S+2C=52

• 3S+C=52

  3S+2C=38

• 3C+S=38

  3C+2S=52

• 3C+S=52

  3C+2S=38

Tags

CCSS.HSA.CED.A.3

Match a sentence with this equation:
 $2B\ +\ 3F\ =\ 22.50$  

• Joe bought 2 burgers and 3 fries for $22.50

• Mary bought 3 burgers and 2 fries for 22.50

• Norman ate 2 burgers and gave away 3 fries in 22.50 minutes

• Ivy bought 2 burgers and 3 fries for 2.20

Tags

CCSS.8.EE.C.8C