Setting Up Word Problems Systems

The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3.

On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156.

Let x represent the number of sundaes sold, and let y represent the number of banana splits sold.

• x + y = 156

  x = y + 8

• x + y = 156

  y = x + 8

• 2x + 3y = 156

  x = y + 8

• 2x + 3y = 156

  y = x + 8

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

Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters.

• x + y = 15

  y = x + 3

• x + y = 15

  x = y + 3

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

Linda is playing a game.

On each turn that she takes, she can earn 2 points or 3 points.

She has taken 16 turns and has earned a total of 34 points.

Which system could be used to determine the number of 2 point turns and 3 point turns Linda had. Let x represent 2 point turns.

Let y represent 3 point turns.

• x + y = 16

  2x + 3y = 34

• x + y = 34

  2x + 3y = 16