Applications of Linear Systems

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.

• a + c = 21
  6a + 4c = 104
• a + c = 104
  6a + 4c = 21
• a + c = 21
  6c + 4a = 104
• a + c = 104
  6c + 4a = 21

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CCSS.HSA.CED.A.3

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? Let "c" represent the # of people who ordered chicken and "s" represent those who ordered steak.

• c + s = 6
  14.80c + 17s = 91
• c + s = 91
  14.80c + 17s = 6
• c + s = 6
  14.80s + 17c = 91
• c + s = 91
  14.80s+ 17c = 6

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CCSS.HSA.CED.A.3

Beyonce wanted to host a barbecue for Spring Break next week. A package of hot dogs cost $1.60, and a package of hamburgers costs $5. Beyonce bought a total of 8 packages of meat and spent $23 total. Write a system for this situation. Assume "x" represents # of hot dog packages and "y" represent # of hamburger packages.

• x + y = 8
  1.60x + 5y = 23
• x + y = 23
  1.60x + 5y = 8
• x + y = 8
  1.60y + 5x = 23
• x + y = 23
  1.60y + 5x = 8

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CCSS.8.EE.C.8C

Michelangelo decided to order Pizza Hut last night. He purchased 3 pizzas and 2 orders of breadsticks for a total of $29.50. Donatello ordered 2 pizzas and 3 orders of breadsticks last Sunday for a total of $23. Set up a system. Let "p" represent the price per pizza and "b" represent the price of an order of breaksticks.

• 3p + 2b = 29.50
  2p + 3b = 23
• 3p + 2b = 23
  2p + 3b = 29.50
• 3b + 2p = 29.50
  2b + 3p = 23
• 5bp = 29.50
  5bp = 23

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CCSS.HSA.CED.A.3

Enterprise charges to rent compact cars for a fixed amount per day plus a fixed amount for each mile driven. Batman rented a car for 6 days, drove it 550 miles and spent $337. Superman rented the same car for 3 days, drove for 350 miles and spent $185. Set up the system. Let "d" represent the fixed charge per day and "m" represent the cost per mile.

• 6d + 550m = 337
  3d + 350m = 185
• 6d + 550m = 185
  3d + 350m = 337
• 6m + 550d = 337
  3m + 350d = 185
• 6m + 550d = 185
  3m + 350d = 337

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CCSS.HSA.CED.A.3

Peyton Manning is comparing two weekend resort specials to relax at now that he has retired. Package A offers a 2-night stay and 3 meals that costs $195. Package B offers a 3-night stay and 5 meals that costs $300. Let "x" represent the cost per night and "y" represent the cost per meal.

• 2x + 3y = 195
  3x + 5y = 300
• 2x + 3y = 300
  3x + 5y = 195
• 2y + 3x = 195
  3y + 5x = 300
• 2y + 3x = 300
  3y + 5x = 195

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CCSS.8.EE.C.8C

You and a friend went to Los Tios for lunch. You order 2 tacos and 2 enchiladas. Your friend ordered 3 tacos and 1 enchilada. Your friend's bill was $4.00. You paid $4.80. Let "t" represent the price per taco and "e" represent the price per enchilada.

• 2t + 2e = 4.80
  3t + e = 4.00
• 2t + 2e = 4.00
  3t + e = 4.80
• 2e + 2t = 4.80
  3e + t = 4.00
• 2e + 2t = 4.00
  3e + t = 4.80

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CCSS.8.EE.C.8C

Captain America wanted to put on a community bake sale. He purchased 12 pounds of sugar and 15 pounds of flour. Iron Man noticed that they needed more ingredient and purchased 4 pounds of sugar and 10 pounds of flour. Iron Man spent $4.60, and Captain America spent $9.30. Let "s" represent the cost per pound of sugar and "f" represent the cost per pound of flour.

• 12s + 15f = 9.30
  4s + 10f = 4.60
• 12s + 15f = 4.60
  4s + 10f = 9.30
• 12f + 15s = 9.30
  4f + 10s = 4.60
• 12f + 15s = 4.60
  4f + 10s = 9.30

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CCSS.HSA.CED.A.3