Creating Equations and Systems

Create a system to answer this:

Meal tickets at the circus cost $4.00 for children and $12.00 for adults. If 1,650 meal tickets were bought for a total of $14,200, how many children and how many adults bought meal tickets?

• c + a = 14200

  4c + 12a = 1650

• c + a = 1650

  c + a = 14200

• 1650 + c = 14200

  4 + 12 = a

• c + a = 1650

  4c + 12a = 14200

Create a system to answer this:

Jamal is choosing between two truck-rental companies. The first, Keep on Trucking, Inc., charges an up-front fee of $20, then 59 cents a mile. The second, Move It Your Way, charges an up-front fee of $16, then 63 cents a mile. When will Keep on Trucking, Inc. be the better choice for Jamal?

• 0.59m + 0.63m = C

  20 + 16 = C

• C = 0.59m + 20

  C = 0.63m + 16

• 59m + 63m = C

  20 + 16 = C

• C = 59m + 20

  C = 63m + 16

The total height of a building, b, and the antenna tower on top o f it, is 425 feet. The difference in heights of the building and the antenna tower is 324 feet. What is the height of the antenna tower?

• b - t = 425

  b + t = 324

• b + t = 425

  b - t = 324

• b + t = 425

  b + t = 324

• b - t = 425

  b - t = 324

Create a system to answer this:

At the baseball stadium, four hot dogs and three bags of candy cost $14.37. Twelve hot dogs and nine bags of candy cost $24.74. What does a hot dog cost?

• 12h + 9c = 24.74

  4h + 3c = 14.37

• 4h + 3c = 24.74

  12h + 9c = 14.37

• h + c = 24.74

  4h + 3c = 14.37

• 4h + 3c = 24.74

  h + c = 14.37

Create a system to answer this:

A craft store has 12 identical sacks of loose buttons. Each button is perfectly circular and is either solid black, b, or solid white, w. Each sack contains 9 more black buttons than white ones. The total number of buttons in all of the sacks is 372. How many buttons of each color are in 1 sack?

• b + w = 9

  12(b + w) = 372

• b - w = 9

  12(b + w) = 372

• w - b = 9

  12(b + w) = 372

• b + w = 9

  12(b + w) = 372

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

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

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

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

________________ is a set of two or more equations that have the same variables.

• solution of a system

• elimination method

• system of equations

• table