System Word Problems Linear

Write the linear inequality in standard form for this situation: The New Kent High School science department can spend no more than $2700 on textbooks next year. The department needs to buy both Biology text books, which cost $57 each, and Chemistry textbooks, which cost $72 each.

• 57x + 72y ≥ 2700

• 57x + 72y > 2700

• 57x + 72y < 2700

• 57x + 72y ≤ 2700

New York City is a popular field trip destination.  This year the senior class at Addison Trail and the senior class at Willowbrook both planned trips there.  The senior class at Addison Trail rented and filled 5 vans and 12 buses with 330 students.  Willowbrook rented and filled 12 vans and 11 buses with 347 students.  Every van had the same number of students in it as did the buses.  How many students can a van carry?  How many students can a bus carry? What should the two equations be for this problem if x = number of students per van and y = number of students per bus?

New York City is a popular field trip destination.  This year the senior class at Addison Trail and the senior class at Willowbrook both planned trips there.  The senior class at Addison Trail rented and filled 5 vans and 12 buses with 330 students.  Willowbrook rented and filled 12 vans and 11 buses with 347 students.  Every van had the same number of students in it as did the buses.  How many students can a van carry?  How many students can a bus carry?

How should we label the variables for this problem?

• x = number of vans

  y = number of buses

• x = number of AT students

  y = number of WB students

• x = number of students in a van

  y = number of students in a bus

• y = 20

• y = 24

• y = 25

• y = 30

Our system of equations for this problem is 5x+12y=330 12x+11y=347 We found that the value of y = 25. What is the value of x if y = 25?

• x = 5

• x = 6

• x = 7

• x = 8

New York City is a popular field trip destination.  This year the senior class at Addison Trail and the senior class at Willowbrook both planned trips there.  The senior class at Addison Trail rented and filled 5 vans and 12 buses with 330 students.  Willowbrook rented and filled 12 vans and 11 buses with 347 students.  Every van had the same number of students in it as did the buses.  How many students can a van carry?  How many students can a bus carry?

• 25 students per van

  and

  6 students per bus

• 25 buses and 6 vans

• 6 buses and 25 vans

• 6 students per van

  and

  25 students per bus

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. Solve the system:
x + y = 21
6x + 4y = 104

• (10, 11)

• (12, 9)

• (11, 10)

• (9, 12)

4x +  8y = 20
-4x + 2y = -30
Which variable will be eliminated?

• The  x

• The  y

• The  z

• The unknown

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?

• x + y = 15
  4x + 2y = 44

• 4x + 2y = 15
  x + y = 44

• x = 2y + 44
  4x = y + 15

• 2x - 4y = 44
  x - y = 15

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have?  Which system best represents the situation? 

• x + y = 1430
  20x + 50y = 49

• x + y = 49
  10x + 5y = 1430 

• x + y = 49
  20x + 50y = 1430

• x + y = 49
  x + y = 1430