Translating Real-World Scenarios into Two Variable Inequalities

This video tutorial teaches how to write systems of two-variable inequalities from word problems. It covers various examples, including Chef LCA's food purchase, Sam's clothing shopping, a pizzeria's earnings, a math club event, and Jake's exercise routine. The video emphasizes defining variables, setting up inequalities, and finding solutions that satisfy all conditions. The tutorial prepares viewers for graphing these systems in a subsequent video.

What is the primary focus of this video?

• Graphing systems of inequalities

• Writing systems of inequalities from word problems

• Solving equations

• Learning about linear functions

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If Chef Luca wants to spend no more than $220 and buy at least 40 pounds of chicken, which inequality represents his spending constraint?

• 2X + 5Y ≤ 220

• 2X + 5Y ≥ 220

• 2X + 5Y = 220

• 2X + 5Y < 220

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In Chef Luca's problem, what does the variable X represent?

• Pounds of steak

• Dollars spent on steak

• Pounds of chicken

• Dollars spent on chicken

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CCSS.HSA.SSE.A.1

Sam wants to buy at least 3 more shirts than shorts. Which inequality represents this condition?

• X > Y + 3

• X = Y + 3

• X ≤ Y + 3

• X ≥ Y + 3

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If Sam wants to spend less than $150 on t-shirts and shorts, which inequality represents her spending constraint?

• 20X + 15Y < 150

• 20X + 15Y ≤ 150

• 20X + 15Y > 150

• 20X + 15Y = 150

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CCSS.HSA.CED.A.2

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A local pizzeria earns between $2,000 and $5,000 a day. Which compound inequality represents this earning range?

• 2000 < 2.50X + 16Y < 5000

• 2000 ≤ 2.50X + 16Y ≤ 5000

• 2000 > 2.50X + 16Y > 5000

• 2000 = 2.50X + 16Y = 5000

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CCSS.HSA.CED.A.1

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For the math club's event, if they sell 160 student tickets, what is the maximum number of adult tickets they can sell?

• 60

• 30

• 40

• 50

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If the math club sells 160 student tickets and 40 adult tickets, will they meet their goal of making at least $800?

• No, they will make exactly $800

• Yes, they will make more than $800

• Yes, they will make exactly $800

• No, they will make less than $800

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Jig wants to burn at least 650 calories but does not want to walk more than 2 hours. Which inequality represents his walking constraint?

• X + Y > 2

• X + Y < 2

• X + Y ≥ 2

• X + Y ≤ 2

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CCSS.HSA.CED.A.3

If Jig jogs for half an hour, what is the minimum number of hours he must walk to meet his goal of burning at least 650 calories?

• 2 hours

• 1.33 hours

• 1.5 hours

• 1 hour

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