Systems of Equations Word Problems

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

Tags

CCSS.HSA.CED.A.3

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

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

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

Dennis mowed his next door neighbor’s lawn for a handful of dimes (.10) and nickels (.05), 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. How many nickels and dimes did Dennis earn?

• 40 nickels, 40 dimes

• 52 nickels, 28 dimes

• 28 nickels, 52 dimes

• 30 nickels, 50 dimes

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)