How to Solve Venn Diagram Problems with Three Categories

TL;DR

To solve Venn diagram word problems with three categories, identify the numbers studying each subject and subtract overlapping values from each section. For instance, if 10 students study all three subjects, adjust the counts for those studying just two subjects accordingly. The total number of students can be found by summing all unique counts, including those outside the circles.

Transcript

today we're going to focus on solving word problems that deal with venn diagrams contained in three categories so let's work on this problem in a certain class of sophomores 46 students are studying algebra 39 are studying biology and 37 are studying chemistry 17 students are studying algebra and bio 15 are studying bio and chem and 18 are studying... Read More

Key Insights

• 🔨 Venn diagrams are a useful tool for visualizing relationships between multiple categories.
• #️⃣ To find the number of students studying a specific combination of subjects, subtract the overlapping sections from the given numbers.
• #️⃣ The total number of students surveyed is obtained by adding up all the numbers in the Venn diagram, including those outside the circles.

Questions & Answers

Q: How do you determine the number of students studying algebra and biology but not chemistry?

In the Venn diagram, we subtract the number of students studying all three subjects (10) from the number of students studying algebra and biology (17), which gives us the answer of 7.

Q: How do you determine the number of students studying biology and chemistry but not algebra?

By subtracting the number of students studying all three subjects (10) from the number of students studying biology and chemistry (15), we find that 5 students are studying biology and chemistry but not algebra.

Q: How many students are studying algebra only?

To find the number of students studying algebra only, subtract the numbers of students studying all three subjects (10), algebra and biology (7), and algebra and chemistry (8) from the total number of students studying algebra (46). This gives us the answer of 21.

Q: What is the total number of students surveyed in the class?

By adding up all the numbers in the Venn diagram, including the students not studying any of the three subjects (18), we find that the total number of surveyed students is 100.

Summary & Key Takeaways

• The video explains how to solve word problems using Venn diagrams with three categories.

• Students studying algebra, biology, and chemistry are represented in the diagram.

• Various scenarios are presented, such as determining the number of students studying specific subjects or combinations of subjects.