Setting Up System of Equations Word Problems

Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?

• 5f + 3g = 5.70

  2f + 10g = 3.60

• 5f + 3g = 3.60

  2f + 10g = 5.70

• 3f + 5g = 5.70

  10f + 2g = 3.60

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, m, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• m + n = 54

  m = 3n + 8

• m + n = 54

  n = 3m + 8

• m + n = 8

  m = 3n + 54

Maricella has a bag containing 35 nickels and quarters. The total value of these coins is $2.50.

• n + q = 35

  .05n + .25q = 2.50

• n + q = 2.50

  .05n + .25q = 35

• n + q = 35

  .5n + .25q = 2.50

• n + q = 2.50

  .5n + .25q = 35

Rachel buys 3 tricycles and 4 bicycles for a total of $72. Joe bought 5 tricycles and 2 bicycles for $50.  Which system models this scenario?

• 3B + 4T = 72
  2T + 5B = 50
• 3T + 4B = 72
  5T + 2B = 50
• 3T + 4B = 50
  5T + 2B = 72

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

Sam has a total of 15 bikes and skateboards.  A bike has 2 wheels and a skateboard has 4 wheels, and she has a total of 40 wheels.  Which system models this scenario?

• B + S = 40
  2B + 4S = 15
• B + S = 15
  2B + 4S = 40
• B + S = 15
  4B + 2S = 40

Ben ordered 20 total items consisting of pizza and sodas.  A pizza is $10, a soda is $2, and he spent a total of $72.  Which system models this scenario?

• 10P + 2S = 20
  P + S = 72
• P + S = 20
  2P + 10S = 72
• P + S = 20
  10P + 2S = 72

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