Setting Up Word Problems Systems

An electronic store advertised a 19-inch model TV for $349 and a 25-inch model for $469. During one month they sold 44 TVs total and profited an amount of $17,516. If x represents the number of 19-inch TVs and y represents the number of 25-inch TVs, which system of equations best describes this situation?

• x + y = 44

  349x + 469y = 17, 516

• x + y = 44

  19x + 25y = 17,516

• 349x + 469y = 44

  x + y = 17, 516

• 19x + 25y = 44

  349x + 469y = 17, 516

The sum of two unknown numbers is -21, and the difference between the two unknown numbers is 3. Which system of linear equations could be used to find the two unknown numbers x and y?

• A

• B

• C

• D

Jon has a total of 25 quarters and dimes. The amount of money he has is $5.65. Which system models this scenario?

• Q + D = 25

  .25Q + .10D = 5.65

• Q + D = 5.65

  .25Q + .10D = 25

• .25Q + .10D = 25

  Q + D = 5.65

The length of a rectangle is two times the width. The perimeter of the rectangle is 24 cm. How would you set up this system of equations?

• L = 2 + w

  2L + 2w = 24

• L = 2w

  L + w = 24

• L = 2w

  2L + 2w = 24

Uncle Freddy rented a total of 12 movies and games.  A movie rents for $3 and a game rents for $4.50, for a total of $42.  Which system models this scenario?

• 3M + 4.50G = 42
  M + G = 12

• 3M + 4.50G = 12
  M + G = 42

• M + G = 12
  4.50M + 3G = 42

Emma has 42 coins in her purse consisting of quarters and dimes. She has a total of $7.95.

• 0.25q + 0.1d = 7.95
  q + d = 42

• 25q + 10d = 7.95
  q + d = 42

• 0.25q + 0.1d = 42
  q + d = 7.95

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

At a local concert hall, the owner charges $7 per ticket. The owner must pay his band $1200. Every customer receives a brochure that costs the owner $2 for each person.

What system would determine when he breaks even?

• y = 7x

  y = 2x + 1200

• y = 2x

  y = 7x + 1200

• y = 9x + 1200

• y = -2x - 1200

  y = 7x

John was 20 feet away and was running 5 feet per minute. Alex was 50 feet away and was 3 feet per minute. Write a system of two equations for this situation?

• y = 5x + 20

  y = 3x + 50

• y = 20x + 5

  y = 50x + 3

• y = 5x + 50

  y = 2x + 20

• y = 50x + 5

  y = 20x + 3

The little bunny ate 20 carrots and he could eat another 5 carrots a day. The big bunny had already eaten 60 carrots and he could eat 25 more carrots a day. Write a system of equations for this situation.

• y = 5x + 20

  y = 25x + 60

• y = 20x + 5

  y = 60x + 25

• y = 60x + 5

  y = 20x + 25

• y = 5x + 60

  y = 25x + 20