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Nov. 14 - Inequalities in Two Variables

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

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Nov. 14 - Inequalities in Two Variables

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  1. pickle day! 11.14.22 Take out your spiral for a warm-up. Agenda: • Warm-up • Notes: Inequality Word Problems • Group/Regroup Pencil, Calculator, Spiral

  2. Inequalities >>>>>>>>>>>>> >>>>>>>>>>>>>

  3. Warm-up: Write an inequalityin one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase?

  4. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  5. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  6. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  7. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  8. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  9. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  10. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  11. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  12. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  13. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  14. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  15. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  16. Warm-up: Write an inequality in one variable and solve each. Answer the question in a sentence. Megan is saving money for college. She has already saved $1500. Her grandmother is giving her $200 for her birthday. She earns $13 per hour working at Chipotle. If she wants to have at least $3000 saved, how many hours would she need to work at Chipotle? The junior class officers can spend no more than $450 for their ring dance. They have already spent $60 on decorations and $273 on water and snacks. They want to purchase balloons that cost $1.25 each. How many balloons can they purchase? Let x = number of hours working at Chipotle 13x + 1500 + 200 > 3000 13x + 1700 > 3000 13x > 1300 x > 100 Megan will have to work at least 100 hours at Chipotle to save at least $3000. Let x = number of balloons 1.25x + 60 + 273 < 450 1.25x + 333 < 450 1.25x < 117 x < 93.6 They can purchase at most 93 balloons.

  17. Inequality Word Problems (Two-Variable)

  18. 9. Tickets to a play cost $5 at the door and $4 in advance. The theater club wants to raise at least $400 from the play. Write and graph an inequality to show how many tickets the theater club needs to sell. Variables: Inequality: a. If the club sells 40 tickets in advance, how many do they need to sell at the door to reach their goal? b. Will the theater club meet their goal if they sell 20 tickets at the door and 50 tickets in advance? Use the graph to justify your answer. c. Identify 3 ticket combinations that would meet the club's goal.

  19. 9. Tickets to a play cost $5 at the door and $4 in advance. The theater club wants to raise at least $400 from the play. Write and graph an inequality to show how many tickets the theater club needs to sell. Variables: Inequality: x = number of tickets at the door y = number of tickets in advance a. If the club sells 40 tickets in advance, how many do they need to sell at the door to reach their goal? b. Will the theater club meet their goal if they sell 20 tickets at the door and 50 tickets in advance? Use the graph to justify your answer. c. Identify 3 ticket combinations that would meet the club's goal. 5x + 4y > 400 The club would need to sell at least 48 tickets at the door to meet the goal. 5x + 4(40)> 400 5x > 240 x > 48 120 100 80 60 40 20 The club would not meet the goal of at least $400 because the ordered pair (20,50) is not in the shaded area of the graph. number of tickets in advance 80 tickets at the door and 40 tickets in advance 50 tickets at the door and 80 tickets in advance 20 tickets at the door and 90 tickets in advance 20 40 60 80 100 120 number of tickets at the door

  20. 10. A storage shelf can hold no more than 250 pounds. Carlos wants to stack boxes of paper that weigh 20 pounds each and computer monitors that weigh 15 pounds each on the shelf. Write and graph an inequality to represent this situation. Variables: Inequality: a. Carlos stacks 8 boxes of paper on the shelf. How many monitors will he be able to put onto the shelf and not go over the weight limit? b. Will Carlos be able to stack 10 boxes of paper and 5 monitors on the shelf? Use the graph to justify your answer. c. Identify 3 combinations of paper boxes and monitors that the shelf can hold.

  21. 10. A storage shelf can hold no more than 250 pounds. Carlos wants to stack boxes of paper that weigh 20 pounds each and computer monitors that weigh 15 pounds each on the shelf. Write and graph an inequality to represent this situation. Variables: Inequality: x = number of boxes of paper y = number of computer monitors a. Carlos stacks 8 boxes of paper on the shelf. How many monitors will he be able to put onto the shelf and not go over the weight limit? b. Will Carlos be able to stack 10 boxes of paper and 5 monitors on the shelf? Use the graph to justify your answer. c. Identify 3 combinations of paper boxes and monitors that the shelf can hold. 20x + 15y < 250 20(8) + 15y < 250 15y < 90 y < 6 Carlos could put up to 6 monitors on the shelf. 24 20 16 12 8 4 number of computer monitors No, he cannot - the point (10,5) is not in the solution region of the graph. 8 boxes of paper and 2 computer monitors 4 boxes of paper and 4 computer monitors 0 boxes of paper and 10 computer monitors 4 8 12 16 20 24 number of boxes of paper

  22. Let’s Group and Regroup!

  23. 1. Betty has ordered an Uber to get to work. She might stop at the Dunkin drive in on the way to get coffee for her co-workers that cost $2.50 each. The cost for an Uber is $1.50 per mile. Betty has no more than $75 for the taxi ride and coffees. Write and graph the inequality that models this situation. Variables: Inequality: a. If Betty does not stop for coffee, how many miles could she travel in the Uber? b. If Betty walks to work, how many coffees can she buy? (pretend she has a cart to push the coffees to work) c. Can Betty purchase 15 coffees and travel 40 miles to work? Why? d. Name three combinations of coffees and miles that could be possible for Betty.

  24. 1. Betty has ordered an Uber to get to work. She might stop at the Dunkin drive in on the way to get coffee for her co-workers that cost $2.50 each. The cost for an Uber is $1.50 per mile. Betty has no more than $75 for the taxi ride and coffees. Write and graph the inequality that models this situation. Variables: Inequality: x = number of coffees y = number of miles a. If Betty does not stop for coffee, how many miles could she travel in the Uber? b. If Betty walks to work, how many coffees can she buy? (pretend she has a cart to push the coffees to work) c. Can Betty purchase 15 coffees and travel 40 miles to work? Why? d. Name three combinations of coffees and miles that could be possible for Betty. 2.5(0)+1.5y<75 1.5y<75 y<50 2.50x + 1.50y< 75 She could travel 50 miles. 60 50 40 30 20 10 2.5x+1.5(0)<75 2.5x<75 x<30 She could buy 30 coffees. number of miles She cannot - that point is not in the shaded region of the graph. 2.5(15)+1.5(40)>75 20 coffees and 5 miles in the Uber 10 coffees and 10 miles in the Uber 5 coffees and 20 miles in the Uber 10 20 30 40 50 60 number of coffees

  25. 2. A fish market charges $9 per pound for cod and $12 per pound for flounder. Let x = the number of pounds of cod and y = the number of pounds of flounder. The fish market has a daily quota of selling at least $120 of fish. Write and graph the inequality that models this situation. Variables: Inequality: a. If the fish market sells no cod, how many pounds of flounder would they need to sell to make their quota? b. Will the fish market make their quota if they sell 8.75 pounds of cod and 7.5 pounds of flounder? How does the graph support this answer? c. Will the fish market make their quota if they sell 5 pounds of cod and 5.25 pounds of flounder? How does the graph support this answer?

  26. 2. A fish market charges $9 per pound for cod and $12 per pound for flounder. Let x = the number of pounds of cod and y = the number of pounds of flounder. The fish market has a daily quota of selling at least $120 of fish. Write and graph the inequality that models this situation. Variables: Inequality: x = number of pounds of cod y = number of pounds of flounder a. If the fish market sells no cod, how many pounds of flounder would they need to sell to make their quota? b. Will the fish market make their quota if they sell 8.75 pounds of cod and 7.5 pounds of flounder? How does the graph support this answer? c. Will the fish market make their quota if they sell 5 pounds of cod and 5.25 pounds of flounder? How does the graph support this answer? 9x + 12y > 120 9(0)+12y>120 12y>120 y>10 They would have to sell 10 or more pounds of flounder. 12 10 8 6 4 2 Yes, they will make their quota. The graph supports this because the point (8.75, 7.5) is in the shaded region. number of pounds of flounder No, they will not make their quota. The graph supports this because the point (5, 5.25) is not in the shaded region. 3 6 9 12 15 18 number of pounds of cod

  27. Delta Math Time

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