Graphs of systems of inequalities word problem | Mathematics I | High School Math | Khan Academy

TL;DR

Ksenia wants to chop at least 20 vegetables with a time limit of 540 seconds, and the analysis determines that the minimum number of carrots she can chop while achieving her goal is 10.

Transcript

• [Voiceover] "Ksenia wants to chop broccoli "and carrots for a competition. "It takes her the same number of seconds "to chop each carrot, and it takes her the same number "of seconds to chop each broccoli head. "Her goal is to chop at least 20 vegetables "with a time limit of 540 seconds," all right. "The graph below represents the set "of all co... Read More

Key Insights

• 🥢 Ksenia's goal is to chop at least 20 vegetables within 540 seconds.
• 🥢 The graph represents the combinations of carrots and broccoli that she wants to chop and can chop within the given constraints.
• 😫 The solution set for Inequality A (blue area) represents the combinations that fulfill her goal of chopping at least 20 vegetables.
• 😫 The solution set for Inequality B (green area) represents the combinations that fit within the time limit of 540 seconds.
• 😫 The overlap between the solution sets represents the combinations that satisfy both her goal and the time limit.
• 🫥 The minimum number of carrots Ksenia can chop while achieving her goal is 10, as shown by the point of intersection between the two lines.

Questions & Answers

Q: What are the two inequalities represented in the graph?

The two inequalities represented in the graph are Inequality A, which shows the combinations of carrots and broccoli that Ksenia wants to chop to meet her goal of at least 20 vegetables, and Inequality B, which represents the combinations Ksenia can chop within her time limit of 540 seconds.

Q: How is the minimum number of carrots Ksenia can chop determined?

The minimum number of carrots Ksenia can chop is determined by finding the overlap between the solution sets of Inequality A and Inequality B. The point of intersection represents the combination of 10 carrots and 10 broccoli heads, which satisfies both her goal and the time limit.

Q: Can Ksenia achieve her goal with less than 10 carrots?

No, Ksenia cannot achieve her goal with less than 10 carrots. The analysis shows that there is no overlap between the solution sets of Inequality A and Inequality B for any combination with fewer than 10 carrots.

Q: What are the constraints Ksenia needs to meet?

Ksenia needs to meet two constraints: chopping at least 20 vegetables (represented by Inequality A) and staying within the time limit of 540 seconds (represented by Inequality B). The combination of 10 carrots and 10 broccoli heads satisfies both constraints.

Summary & Key Takeaways

• Ksenia has a goal of chopping at least 20 vegetables within a time limit of 540 seconds.

• Inequality A represents the range of all combinations of carrots and broccoli that Ksenia wants to chop.

• Inequality B represents the range of all combinations that Ksenia can chop within her time limit.