Systems of Equations

Bernard spent $5,100 replacing the flooring in his 1,800-square-foot house. He paid $5 per square foot for carpeting and $2 per square foot for vinyl tile. If c represents a square foot of carpeting, and v represents a square foot of vinyl tile, which is a system of equations that could be used to determine the amount of each material he used?

• c + 5v = 1,800
  c + 2v = 5,100

• c + v = 5,100
  5c + 2v = 1,800

• c + v = 1,800
  5c + 2v = 5,100

• c + 5v = 5,100
  c + 2v = 1,800

Tags

CCSS.8.EE.C.8C

A local kennel has twice as many cats (c) as dogs (d). When full, the kennel has a total of 30 cats and dogs. Which system of equations could be used to find the number of cats in the kennel when it is full?

• d = 2c

  c + d = 30

• c = 2d

  c + d = 30

• c = d − 2

  c + d = 30

• c = d + 2

  c + d = 30

Tags

CCSS.8.EE.C.8C

Ralph spent $132 to buy movie tickets for 20 students and 4 adult chaperones. Adult tickets cost $3 more than student tickets. If A is the price of an adult ticket and S is the price of a student ticket, which system of equations could be used to find the price of each adult and student ticket?

• S = A + 3

  4A + 20S = 132

• A = S + 3

  A + S = 132

• A + S = 3

  20A + 4S = 132

• A = S + 3

  4A + 20S = 132

Tags

CCSS.8.EE.C.8C

Charlie bought jeans, j , and T-shirts, t , at a clothing store. The receipt showed that a total of seven items was purchased and that the jeans were $28 each and the T-shirts were $12 each. If he spent a total of $116 before tax, which system of equations could be used to determine the number of jeans he purchased?

• 7j + 12t = 28

  j + t = 116

• 28j + 12t = 116

  j + t = 7

• 12j + 28t = 116

  j + t = 7

• 28j + 12t = 7

  j + t = 116

Tags

CCSS.HSA.CED.A.3

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

• y = 9.65 + x

  y = 8.40 + x

• y = 9.65x + 43

  y = 8.40x + 58

• y = 9.65x

  y = 8.40x

• y = 9.65x - 43

  y = 8.40x - 58

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza 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 + 0.65x

  y = 7.30 + 0.90x

• x + y = 6.80

  x + y = 7.30

• y = 6.80 + 0.90x

  y = 7.30 + 0.65x

• y + 0.90x = 6.80

  y + 0.65x = 7.30

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 = 49

  20x + 50y = 1430

• x + y = 49

  10x + 5y = 1430

• x + y = 1430

  20x + 50y = 49

• x + y = 49

  x + y = 1430

Tags

CCSS.HSA.CED.A.3