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Nov. 17 - Systems of Inequalities

algebra 1<br>middle school math<br>high school math

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Nov. 17 - Systems of Inequalities

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  1. homemade bread day! 11.17.22 Clear desk except for a pencil, packet from yesterday and a calculator. Complete question #3 from the packet. Agenda: • Warm-up • More Systems Notes • Practice: Systems of Inequalities Best bread choice? Pencil, Calculator, Spiral

  2. It works the same way with three. The solution is the overlap of all three shaded regions!!

  3. It works the same way with three. The solution is the overlap of all three shaded regions!!

  4. It works the same way with three. The solution is the overlap of all three shaded regions!!

  5. It works the same way with three. The solution is the overlap of all three shaded regions!!

  6. It works the same way with three. The solution is the overlap of all three shaded regions!!

  7. It works the same way with three. The solution is the overlap of all three shaded regions!!

  8. It works the same way with three. The solution is the overlap of all three shaded regions!!

  9. It works the same way with three. The solution is the overlap of all three shaded regions!!

  10. It works the same way with three. The solution is the overlap of all three shaded regions!!

  11. It works the same way with three. The solution is the overlap of all three shaded regions!!

  12. It works the same way with three. The solution is the overlap of all three shaded regions!!

  13. It works the same way with three. The solution is the overlap of all three shaded regions!!

  14. It works the same way with three. The solution is the overlap of all three shaded regions!!

  15. It works the same way with three. The solution is the overlap of all three shaded regions!! (0, 0)

  16. It works the same way with three. The solution is the overlap of all three shaded regions!! (0, 0) (-1, 1)

  17. It works the same way with three. The solution is the overlap of all three shaded regions!! (0, 0) (-1, 1) (0, -2)

  18. Systems of Inequalities

  19. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal.

  20. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal.

  21. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1200 a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal.

  22. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1200 6x + 4y > 24 a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal.

  23. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 12 10 8 6 4 2 200x + 100y < 1200 6x + 4y > 24 number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal. 2 4 6 8 10 12 number of adults

  24. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 12 10 8 6 4 2 200x + 100y < 1200 6x + 4y > 24 number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal. 2 4 6 8 10 12 number of adults

  25. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 12 10 8 6 4 2 200x + 100y < 1200 6x + 4y > 24 number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal. 2 4 6 8 10 12 number of adults

  26. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 12 10 8 6 4 2 200x + 100y < 1200 6x + 4y > 24 number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal. 2 4 6 8 10 12 number of adults

  27. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 12 10 8 6 4 2 200x + 100y < 1200 6x + 4y > 24 number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal. 2 4 6 8 10 12 number of adults

  28. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 12 10 8 6 4 2 200x + 100y < 1200 6x + 4y > 24 number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal. 2 4 6 8 10 12 number of adults

  29. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 12 10 8 6 4 2 200x + 100y < 1200 6x + 4y > 24 number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal. Yes, since the point (2, 5) is in the overlapping shaded region, it satisfies both inequalities. Therefore, they can all participate together. 2 4 6 8 10 12 number of adults

  30. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 12 10 8 6 4 2 200x + 100y < 1200 6x + 4y > 24 number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal. Yes, since the point (2, 5) is in the overlapping shaded region, it satisfies both inequalities. Therefore, they can all participate together. 3 adults and 4 children 2 4 6 8 10 12 number of adults

  31. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 12 10 8 6 4 2 200x + 100y < 1200 6x + 4y > 24 number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal. Yes, since the point (2, 5) is in the overlapping shaded region, it satisfies both inequalities. Therefore, they can all participate together. 3 adults and 4 children 1 adult and 7 children 2 4 6 8 10 12 number of adults

  32. Problem 4: Natalie runs the bounce house at a fall festival. The bounce house can hold a maximum of 1200 pounds at one time. She estimates that an adult weighs about 200 pounds and children weigh about 100 pounds. For each session of bounce time, Natalie charges adults $6.00 each and children $4.00 each. Natalie hopes to make at least $24 for each session. Variables: Inequalities: x = number of adults y = number of children 12 10 8 6 4 2 200x + 100y < 1200 6x + 4y > 24 number of children a. A family of two adults and five children would like a turn in the bounce house. Can they all participate together? Explain. b. Name three combinations of adults and children that can be in the bounce house and allow Natalie to reach her goal. Yes, since the point (2, 5) is in the overlapping shaded region, it satisfies both inequalities. Therefore, they can all participate together. 3 adults and 4 children 1 adult and 7 children 0 adults and 9 children 2 4 6 8 10 12 number of adults

  33. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time.

  34. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time.

  35. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time.

  36. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time.

  37. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children number of adults

  38. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children 2 4 6 8 10 12 number of adults

  39. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children 2 4 6 8 10 12 number of adults

  40. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children 2 4 6 8 10 12 number of adults

  41. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children 2 4 6 8 10 12 number of adults

  42. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children 2 4 6 8 10 12 number of adults

  43. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children 200x + 100y < 1500 200(3)+100(4)<1500 600 + 400 < 1500 1000 < 1500 True 2 4 6 8 10 12 number of adults

  44. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children 200x + 100y < 1500 200(3)+100(4)<1500 600 + 400 < 1500 1000 < 1500 True x + y < 8 3 + 4 < 8 7 < 8 True 2 4 6 8 10 12 number of adults

  45. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children Only one more person can get in and keep the second inequality true. It can be either an adult or a child and will still keep the first inequality true. 200x + 100y < 1500 200(3)+100(4)<1500 600 + 400 < 1500 1000 < 1500 True x + y < 8 3 + 4 < 8 7 < 8 True 2 4 6 8 10 12 number of adults

  46. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children Only one more person can get in and keep the second inequality true. It can be either an adult or a child and will still keep the first inequality true. 200x + 100y < 1500 200(3)+100(4)<1500 600 + 400 < 1500 1000 < 1500 True x + y < 8 3 + 4 < 8 7 < 8 True 1 adult and 3 children 2 4 6 8 10 12 number of adults

  47. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children Only one more person can get in and keep the second inequality true. It can be either an adult or a child and will still keep the first inequality true. 200x + 100y < 1500 200(3)+100(4)<1500 600 + 400 < 1500 1000 < 1500 True x + y < 8 3 + 4 < 8 7 < 8 True 1 adult and 3 children 1 adult and 6 children 2 4 6 8 10 12 number of adults

  48. Problem 5: The maximum capacity for an average passenger elevator is 8 people and 1500 pounds. It is estimated that adults weigh about 200 pounds and children weigh about 100 pounds. Variables: Inequalities: x = number of adults y = number of children 200x + 100y < 1500 x + y < 8 18 15 12 9 6 3 a. If 3 adults and 4 kids are in the elevator, can anyone else safely get in? Explain using the inequalities. b. Name three combinations of adults and children that can safely be in the elevator at the same time. number of children Only one more person can get in and keep the second inequality true. It can be either an adult or a child and will still keep the first inequality true. 200x + 100y < 1500 200(3)+100(4)<1500 600 + 400 < 1500 1000 < 1500 True x + y < 8 3 + 4 < 8 7 < 8 True 1 adult and 3 children 1 adult and 6 children 3 adults and 3 children 2 4 6 8 10 12 number of adults

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