Systems of Equations Word Problems Set Up

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

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

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

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? Which set of equations is correctly set up to solve this word problem if x represents # of geese and y represents # of buffalo?

• x+y=64

  4x+2y=20

• x+y=20

  4x+2y=64

• x+y=64

  2x+4y=20

• x+y=20

  2x+4y=64

• 
• 
• 
• 

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same.

Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

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

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