Systems Word Problems

Demetrius and Greta are photographers for the yearbook and trying to get their photos published. Greta got 8 fewer than twice the number of photos published than Demetrius got published. Together, 46 of their photos were published in the yearbook.

Which system of equations models this situation?

• g = 8 - 2d

  g = 46 - d

• d = 8 - 2g

  d + g = 46

• d = 2g - 8

  d = 46 - g

• g = 2d - 8

  g + d = 46

A spiral notebook contains 30 more sheet of paper than a memo book. The total number of sheets of paper in 3 new spiral notebooks and 5 new memo books is 810 sheets. Which system of equations can be used to find, s, the number of sheets of paper in one spiral notebook, and, m, the number of sheets of paper in one memo book?

• s - m = 30

  3s + 5m = 810

• s + m = 30

  3s + 5m = 810

• s - m = 30

  5s + 3m = 810

• s + m = 30

  5s + 3m = 810

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25
  5c + 10d = 16.50
• 10c + 5d = 16.50
  5c + 10d = 14.25
• c + d = 10
  5c + 10d = 16.50
• c + d = 5
  5c + 10d = 16.50

Tags

CCSS.8.EE.C.8C

A piggy bank contains 18 coins consisting of only quarters and dimes. The total value of the coins is $2.85. Which system of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?

• 0.10q + 0.25d = 2.85

  q + d =18

• 0.10q +0.25d = 18

  q + d = 2.85

• 0.25q + 0.10d = 2.85

  q + d =18

• 0.25q + 0.10d = 18

  q + d = 2.85

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

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.  
Solve: x= apples, y= bananas

• (1.75, 1)
• (1.5, 1.17)
• (-10.7, 9.3)
• (1, 1.5)

Tags

CCSS.8.EE.C.8C

1.  The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

• 5q + 2z = 1.32
  1z = 0.75
• 5q + 2z = 1.32
  3q + 1z = 0.75
• q + z = 1.32
  q + z = 0.75
• 5q + 2z = 0.75
  3q + 1z = 1.32

Tags

CCSS.HSA.CED.A.3

What is the solution to the system?

• (3, -1)
• (2, -6)
• No Solution 
• (6, -2)

Tags

CCSS.8.EE.C.8A

Solve the system:

-2x + 4y = 14

4x + 2y = 12

• (1, 4)

• (-3, 4)

• (4, -2)

• (7, -12)

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

Tags

CCSS.8.EE.C.8C