Linear System Word Problems

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

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write a system of equations to represent this situation.

• a + c = 21

  6a + 4c = 104

• a + c = 21

  4a + 6c = 104

• a + c = 104

  6a + 4c = 21

• a + c = 104

  4a + 6c = 21

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 school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52

The table shows the rates for two car ride services.

The total cost, c, is dependent on the number of miles, m, that are traveled. Which of these systems of equations represents this situation? ​ ​ ​ ​ (a)  

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Write a linear system to model this situation.

• t + m = 2.10

  3t + 2m = 5.15

• t + m = 2.10

  2t + 3m = 5.15

• 3t + 2m = 2.10

  t + m = 5.15

• 2t + 3m = 2.10

  t + m = 5.15

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. Write a linear system to represent this situation.

• 7x + y = 175

  6x + 7y = 165

• 7x + 7y = 175

  6x + 7y = 165

• x + y = 175

  6x + 7y = 165

• 7x + 7y = 175

  6x + 6y = 165

The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. Write a linear system to model this situation.

• 11v + 3b = 283

  12v + 14b = 770

• 11v + 3b = 770

  12v + 14b = 283

• 11v + 12b = 283

  3v + 14b = 770

• 14v + 3b = 283

  12v + 11b = 770

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

• 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

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. Write a linear system to model this situation.

• 10x + 9y = 56

  2x + 3y = 60

• 10x + 9y = 60

  2x + 3y = 56

• 10x + 2y = 56

  9x + 3y = 60

• 9x + 3y = 56

  10x + 2y = 60