Math Problem Statement
Solution
The images you uploaded contain information about a coffee survey and related questions. To solve the problem accurately, let's break down the information from both images.
Information Extracted:
-
Survey Details (First Image):
- 221 people like espresso.
- 127 people like cappuccino and chocolate-flavored coffee.
- 182 people like cappuccino.
- 136 people like espresso and chocolate-flavored coffee.
- 209 people like chocolate-flavored coffee.
- 78 people like all three types of coffee.
- 116 people like espresso and cappuccino.
- 82 people like none of these types of coffee.
-
Questions (Second Image):
- a. How many of the customers like only chocolate-flavored coffee?
- b. How many like cappuccino and chocolate-flavored coffee, but not espresso?
- c. How many like espresso and cappuccino, but not chocolate-flavored coffee?
- d. How many like exactly one of the three types of coffee?
Plan for solving:
We can solve this using set theory and Venn diagrams. There are three sets:
- E (espresso lovers)
- C (cappuccino lovers)
- Ch (chocolate-flavored coffee lovers)
By using the principle of inclusion-exclusion and the information provided, we can determine the number of people who fall into each subset.
Would you like me to proceed with solving this step-by-step, including drawing the Venn diagram to illustrate the breakdown?
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Math Problem Analysis
Mathematical Concepts
Set Theory
Venn Diagram
Inclusion-Exclusion Principle
Formulas
Inclusion-Exclusion Principle: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|
Theorems
Inclusion-Exclusion Principle
Suitable Grade Level
Grades 11-12 or introductory college level
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