systems word problems

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?

• 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?

• 2 pigs and 8 ducks

• 10 pigs

• 8 pigs and 2 ducks

• 12 pigs and -3 ducks

There are 20 animals in the barn. Some are geese and some are buffalo. There are 64 legs in all. How many of each animal are there?

• 12 geese and 8 buffalo

• 8 geese and 12 buffalo

• 4 geese and 28 buffalo

• The buffalo all sat on the geese and now there are only 44 legs in all.