Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 24.5 Venn Diagrams to secure good marks & knowledge in the exams.
McGraw-Hill Math Grade 8 Answer Key Lesson 24.5 Venn Diagrams
Exercises
DIAGRAM
Question 1.
Ramon surveyed a group of 50 people at the town meeting about the expansion of the town zoo and the construction of a bike path. He found that of the 50 people he surveyed, 32 people supported expanding the zoo and 30 people supported constructing a bike path. Twelve people supported both projects. Fill in the Venn Diagram to represent the results of the survey.
How many people supported the town zoo only? ____________
How many supported the bike path only? _____________
Answer:
Number of people supported the town zoo only = 20.
Number of people supported the bike only = 18.
Explanation:
Total number of people he surveyed = 50.
Number of people supported expanding the zoo = 32.
Number of people supported constructing a bike path = 30.
Number of people supported both projects = 12.
Total number of people surveyed = Number of people supported expanding the zoo + Number of people supported constructing a bike path
= 32 + 30
= 62.
Number of people supported the town zoo only = Number of people supported expanding the zoo – Number of people supported expanding the zoo
= 32 – 12
= 20.
Number of people supported the bike only = Number of people supported constructing a bike path – Number of people supported both projects
= 30 – 12
= 18.
Question 2.
The manager of the local clothing store wants to know which jeans to stock for the upcoming back-to-school sale. He reviews the numbers from last year’s sale and finds that the store sold 120 pairs of jeans. 80 were boot- cut, and 60 were stone-washed. Assuming the store only stocked those two styles of jeans, how many of the jeans sold were both stone-washed and boot-cut?
How many of the jeans were just stone-washed and not boot-cut? _____________
How many were just boot-cut and not stone-washed? _____________
Complete the Venn Diagram to show the data.
Answer:
Number of people of the jeans were just stone-washed and not boot-cut = 60.
Number of people were just boot-cut and not stone-washed = 40.
Explanation:
Number of pairs of jeans the store sold = 120.
Number of pairs of jeans were boot- cut = 80.
Number of pairs of jeans were stone-washed = 60.
Total number of pairs of jeans were boot- cut and stone-washed = Number of pairs of jeans were boot- cut + Number of pairs of jeans were stone-washed
= 80 + 60
= 140.
Total number of pairs of jeans were both boot- cut and stone-washed = Total number of pairs of jeans were boot- cut and stone-washed – Number of pairs of jeans the store sold
= 140 – 120
= 20.
Number of people of the jeans were just stone-washed and not boot-cut = Number of pairs of jeans were boot- cut – Total number of pairs of jeans were both boot- cut and stone-washed
= 80 – 20
= 60.
Number of people were just boot-cut and not stone-washed = Number of pairs of jeans were stone-washed  – Total number of pairs of jeans were both boot- cut and stone-washed
= 60 – 20
= 40.