Setting Up Word Problems Systems

Dishann mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

• d + n = 6.60
  .10d + .05n = 80

• d + n = 80
  d + n = 6.60

• d + n = 80
  .10d + .05n = 6.60

• d + n = 80
  .05d + .10n = 6.60

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

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales. Which system best represents the situation?

• 4x + 7y = 578

  x + y = 3365

• 4x + 7y = 3365

  x + y = 578

• 4y + 7x = 578

  x + y = 3365

• 4y - 7x = 3365

  x - y = 578

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 system of equations could you use to determine the number of shirts sold 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

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

• 5q + 2z = 1.32
  1z = 0.75

• 5q + 2z = 1.32
  3q + 1z = 0.75

• q + z = 1.32
  q + z = 0.75

• 5q + 2z = 0.75
  3q + 1z = 1.32

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

The sum of Mr. Micklow and Ms. Craft's age is 55.  The difference is 3.  Which system of equations represents the situation?

• 2x + 3y = 55
  2x + 5y = 3

• x + y = 55
  x - y = 3

• x + y = 3
  x - y = 55

• (2, -2)
• (2, 2)
• (-2, 2)
• (-2, -2)

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

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