Writing Systems of Equations

Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. 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

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

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

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations that represents this situation. Let q represent the number of squash purchased and let z represent the number of zucchini purchased.

• 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

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. Let h represent the number of haircuts given and d represent the number of hair dyes done. 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

A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. 

Which systems of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?

Tags

CCSS.8.EE.C.8C

There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or 12 inches. The diameter of all 15 plates combined is 140 inches.

Which system of equations can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?

Tags

CCSS.HSA.CED.A.3

You have a total of 17 coins.  All of your coins are nickels and dimes.  The total value of the coins is $1.35.  Which system of equations represents this situation?

• n+d=17
  .05n+.10d=1.35
• .05n+.10d=17
  n+d=1.35
• .25n+.10d=1.35
  n+d=17

Tags

CCSS.HSA.CED.A.3

At a restaurant, the cost for 2 burritos and 1 tortilla salad is $20.57. The cost for 3 burritos and 3 tortilla salads is $36.24. Which pair of equations can be used to determine b, the cost of a burrito, and t, the cost of a tortilla salad?

• b + t = 20.57

  
  

  3b + 3t = 36.24

• 2b + t = 20.57

  
  

  3b + 3t = 36.24

• 2b + t = 20.57

  
  

  b + t = 36.24

• b + 2t = 20.57

  
  

  b + t = 36.24

Tags

CCSS.8.EE.C.8C