Systems of Equations: Word Problems

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 

• x + y = 6
  14.80x + 17y = 91
• x + y = 91
  14.80x + 17y = 6
• x + y = 6
  14.80y + 17x = 91
• x + y = 91
  14.80x+ 17y = 6

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

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

Tags

CCSS.HSA.CED.A.3

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 to represent this situation assuming "a" represents # of adult tickets and "c" represents # of children's tickets.

• x + y = 21
  6x + 4y = 104
• x + y = 104
  6x + 4y = 21
• x + y = 21
  6y + 4x = 104
• x + y = 104
  6x + 4y = 21

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

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)

Tags

CCSS.8.EE.C.8C

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation? *

• 1.5x + 0.5y = 78.5
  x + y = 87
• 1.5x + 0.5y = 78.5
  1.5x + 0.5y = 87
• x + y = 78.5
  1.5x + 0.5y = 87
• x + y = 78.5
  x + y = 87

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• (35, 52)
• (18, 69)
• ( 52, 35) 
• (61, 26)

Tags

CCSS.8.EE.C.8C

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

• 10 horses, 18 chickens
• 16 horses, 12 chickens
• 12 horses, 16 chickens
• 18 horses, 10 chickens

Tags

CCSS.8.EE.C.8C

What is the solution to this system of linear equations? 
Use substitution.

y = -2x - 6
-2x + y = 6

• (0, -3)
• (-3, -12)
• (-3, 0)
• (3, -12)

Tags

CCSS.HSA.REI.C.6

What is the value of x in the solutiont o this system of linear equations?
Use substitution.

y = -3x + 3
- 2x + 2y  = 6

• 0
• No solution
• 4
• - 4

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.11