Word Problems for Systems

Josh is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?

• x - y = -10
  x + y = -2
• x = -2 
  y = 5
• x + y = -2
  x - y = -10
• x + y = -10
  x - y = -2

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 talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3
• x + y = 33
  x = 2y - 3
• x + y = 33
  x = 3 - 2y
• x + y = 3
  x = 33 - 2y

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.

To solve, I graphed:

x + y = 21

6x + 4y = 104

I got an intersection point at (10,11). What does that mean in context of the problem?

• There are 10 adults and 11 children.

• There are 11 adults and 10 children.

• The adults are $10 and the children are $11.

• There are 104 adults and 21 children.

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

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

In a pasture are horses and chickens if there are a total of 28 animals and 80 legs how many chickens and horses? Which equations are set up to solve this word problem if x represents # of horses and y represents # of chickens?

• 2x + 4y = 28

  x+y = 80

• 4x + 2y = 80

  x+y = 28

• 2x + 4y = 80

  x+y = 28

• 4x + 2y = 28

  x+y = 80

In a pasture are horses and chickens if there are a total of 28 animals and 80 legs how many chickens and horses?

• 10 horses, 18 chickens

• 16 horses, 12 chickens

• 12 horses, 16 chickens

• 18 horses, 10 chickens

A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there? Which set of equations is correctly set up to solve this word problem if x represents # of pigs and y represents # of ducks?

• x+y=10

  4x+2y=36

• x+y=36

  4x+2y=10

• x+y=10

  2x+4y=36

• x+y=36

  2x+4y=10