Writing Systems of Equations

Nancy went to the grocery store. 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

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

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

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

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

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

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

• 1.5N+0.5S=78.5

  N+S=87

• 1.5N+0.5S=78.5

  1.5N+0.5S=87

• N+S=78.5

  1.5N+0.5S=87

• N+S=78.5

  N+S=87

• 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

• JB's Deli charges $ 0.75 for each pizza and $3.00 per topping

• Sally's Pizza  charges $3.00 per pizza with a $7.50 delivery fee

• Pizza Time charges $7.50 for each pizza and $.30 for the delivery fee

• Pizza Planet charges $7.50 per pizza with a $3.00 delivery fee

The perimeter of a rectangle is forty inches. The length is two inches more than three times the width.

• 2L + 2w = 40

  L = 3w + 2

• 2L + 2w = 40

  w = 3L + 2

• 2L + 2w = 40

  L = 2w + 3

• 2L + 2w = 40

  w = 2L + 3