Writing Systems of Linear Equations

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?

• x + y = 15
  4x + 2y = 44
• 4x + 2y = 15
  x + y = 44
• x = 2y + 44
  4x = y + 15
• 2x - 4y = 44
  x - y = 15

Tags

CCSS.8.EE.C.8C

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3
• x + y = 33
  x = 2y - 3
• x + y = 33
  x = 3 - 2y
• x + y = 3
  x = 33 - 2y

Tags

CCSS.HSA.CED.A.3

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

• 4x + 6y = 3

  13.5x - 13y = 6

• x + y = 4

  x - y = 6

• 4x + 6y = 13

  3x + 7y = 13.5

• 4x - 6y = 13

  3x - 7y = 13.5

Tags

CCSS.8.EE.C.8C

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out (all) the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels? (Hint: How much are the coins worth?)

• d + n = 6.60

  .10d + .05n = 80

• d + n = 80

  d + n = 6.60

• d + n = 80

  .10d + .05n = 6.60

Tags

CCSS.8.EE.C.8C

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, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530

Tags

CCSS.HSA.CED.A.3

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54

  t = 3n + 8

• t + n = 54

  n = 3t + 8

• t + n = 54

  t = 3n - 8

• t + n = 8

  t = 3n + 54

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. How many of each bill does Caitlin have? Which system best represents the situation?

• x + y = 1430

  20x + 50y = 49

• x + y = 49

  10x + 5y = 1430

• x + y = 49

  20x + 50y = 1430

• x + y = 49

  x + y = 1430

Tags

CCSS.HSA.CED.A.3

A large pizza at Palanzio’s Pizzeria (c) costs $6.80 plus $0.90 for each topping.The cost of a large cheese pizza at Guido’s Pizza (c) is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

• y = 6.80 + .65x

  y=7.30+.90x

• x + y = 6.80

  x + y = 7.30

• y = 6.80+.90x

  y = 7.30 + .65x

Tags

CCSS.8.EE.C.8C

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

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

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