Writing Systems of Linear Equations

The Maplewood Symphony Orchestra sold 146 tickets and collected a total of $1036 in ticket sales. Admission was $5 for children and $8 for adults. Write two equations that would be used to solve the system.

• c+a=146

  5c+8a=1036

• c-a=146

  8c+5a=1036

• c+a=1036

  8c+5a=146

• c+a=146

  5c-8a=1026

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The manager of a movie theater wants to know the number of adults and children who go to the movies. The theater charges $8 for each adult and $4 for each child. At a showing where 200 tickets were sold, the theater collected $1304. Write two equations that would be used to solve the system.

• a+c=1304

  8a+4c=200

• a+c=200

  4a+8c=1304

• a+c=200

  8a+4c=1304

• a-c=200

  4a+8c=1304

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J. P. is thinking of two numbers. The sum of the numbers is 163, and their difference is 33. Write two equations that would be used to solve the system.

• x+y=33

  x+y=163

• x+y=163

  x-y=33

• x-y=33

  x-y=163

• x+y=33

  x-y=163

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The school’s photographer took pictures of couples at this year’s prom. She charged $3.25 for wallet-size pictures and $10.50 for portrait-size pictures. Crystal and Dan bought a total of 10 pictures for $61.50. Write two equations that would be used to solve the system.

• 10.50w+3.25p=10

  w+p=61.50

• 3.25w+10.50p=10

  w+p=61.50

• 10.50w+3.25p=61.50

  w+p=10

• 3.25w+10.50p=61.50

  w+p=10

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On Friday, 3247 people attended the county fair. The entrance fee was $5 for adults and $3 for children 12 or under. The fair collected a total of $14,273. Write two equations that would be used to solve the system.

• 3a+5c=3,247

  a-c=14,273

• 5a+3c=14,273

  a+c=3,247

• 3a-5c=3,247

  a+c=14,273

• 5a+3c=3,247

  a+c=14,273

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Each day Mario prepares a large basket of self-serve tortilla chips in his restaurant. On Monday, 40 adults and 15 children ate 10.8 lb of chips. On Tuesday, 35 adult and 22 children ate 12.29 lb of chips. Write two equations that would be used to solve the system so that Mario would know whether adults or children eat more chips on average.

• 15a-40c=12.29

  35a+22c=10.8

• 40a+15c=10.8

  35a+22c=12.29

• 15a+40c=10.8

  35a-22c=12.29

• 40a+15c=12.29

  35a+22c=10.8

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Eric has some quarters and nickels in his pocket. He has 8 more nickels than quarters. The total value is $3.70. Write two equations that could be used to solve the system.

• 0.25q+0.05n=3.70

  q=n+8

• 0.05q+0.25n=3.70

  n=q+8

• 0.25q+0.05n=3.70

  n=q+8

• 0.25q-0.05n=3.70

  n=q-8

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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

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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

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Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

• 3H + 2D = 315

  2H + 4D = 450

• 3H + 2D = 450

  2H + 4D = 315

• 2H + 4D = 315

  3H + 2D = 450

• 3H + 2D = 315

  2H + 2D = 135

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