Setting Up Systems Word Problems

The sum of Teresa’s and Cathy’s weight is 118 pounds. Teresa weighs 26 pounds more than Cathy. If Teresa’s weight is T and Cathy’s weight is C, which of these systems of equations best represents this relationship?

• T + C = 118

  T = 26

• T + C = 118

  T + 26 = C

• T + C = 64

  T - C = 26

• T + C = 118

  T = C + 26

Tags

CCSS.HSA.CED.A.3

The County Buffet restaurant has tables that seat 6 people and booths that can seat 4 people. The restaurant has 38 seating units for seating a total of 188 people. Which system of equations could you use to find the number of tables, t, and the number of booths, b, that are at the restaurant?

• t + b = 38

  6t + 4b = 188

• 4t = 38

  6b = 188

• t + b = 188

  6t + 4b = 38

• t + b = 38

  4t + 6b = 188

Tags

CCSS.8.EE.C.8C

A television weighs 50 pounds and a microwave weighs 30 pounds. A TV occupies 4 cubic feet and a microwave occupies 3 cubic feet. A truck is carrying 1500 pounds of cargo that occupies 138 cubic feet of space. Which system of equations can be used to find the total number of televisions, t, and microwaves, m, that are in the truck?

• 50t + 30m = 138

  4t + 3m = 1500

• 50t + 4m = 1500

  30t + 3m = 138

• 50t + 4t = 1500

  30 + 3m = 138

• 50t + 30m = 1500

  4t + 3m = 138

Tags

CCSS.8.EE.C.8C

The perimeter of a rectangular wooden desk is 90 square feet. The deck’s length is 5 feet less than 4 times the width. Which system of linear equations can be used to determine the length, L , and the width, W, of the wooden desk?

• 2L + 2W = 90

  L = 5 - 4W

• 2L + 2W = 90

  L = 4W - 5

• L + W = 90

  L = 5W - 4

• L + W = 90

  W = 5 - 4L

Tags

CCSS.HSA.CED.A.3

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 + .65x
  y=7.30+.90x

• x + y = 6.80
  x + y = 7.30

• y = 6.80+.90x
  y = 7.30 + .65x

• y + .90x = 6.80
  y + .65x = 7.30

Tags

CCSS.8.EE.C.8C

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

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.

(Let c represent coffee and d represent doughnuts )

• 10c + 5d = 14.25

  5c + 10d = 16.50

• 10c + 5d = 16.50

  5c + 10d = 14.25

• c + d = 10

  5c + 10d = 16.50

• c + d = 5

  5c + 10d = 16.50

Tags

CCSS.8.EE.C.8C

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

Ralph makes $14 per hour plus a $20 bonus.  Melissa makes $12 per hour plus a $15 bonus.  Which system models this scenario?

• y = 14x + 15
  y = 12x + 20

• y = 20x + 14
  y = 15x + 12

• y = 14x + 20
  y = 12x + 15

• 14x + 20y = 1

  12x + 15y = 2

Tags

CCSS.8.EE.C.8C

A large pizza at Pesaro’s Pizzeria costs $6.80 plus $0.90 for each topping.The cost of a large cheese pizza at Marcello’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 + .65x

  y=7.30+.90x

• x + y = 6.80

  x + y = 7.30

• y = 6.80+.90x

  y = 7.30 + .65x

• y + .90x = 6.80

  y + .65x = 7.30

Tags

CCSS.8.EE.C.8C