We surveyed
440
440 people. We asked: Do you support the Dodgers? Do you support the Angels? Here are the results:

220
220 people did not support either team.
57
57 people support both teams.
82
82 support the Angels, but not the Dodgers.
A total of
301
301 do not support the Angels.

Find
a
a​,
b
b​,
c
c​, and
d
d​.
a
=
a=
people
Preview

b
=
b=
people
Preview

c
=
c=
people
Preview

d
=
d=
people
Preview

We can represent this survey data using a Venn diagram approach, where:

- \( a \) represents the people who support only the Dodgers.
- \( b \) represents the people who support both the Dodgers and the Angels.
- \( c \) represents the people who support only the Angels.
- \( d \) represents the people who do not support either team.

We are given the following information:

- Total number of people surveyed: 440
- Number of people who do not support either team: \( d = 220 \)
- Number of people who support both teams: \( b = 57 \)
- Number of people who support only the Angels: \( c = 82 \)
- Total number of people who do not support the Angels: \( 301 \)

Let's break down how to find the values of \( a \), \( b \), \( c \), and \( d \).

### Step 1: Finding \( d \)
We are already given that 220 people do not support either team:
\[
d = 220
\]

### Step 2: Finding \( b \)
We are told that 57 people support both the Dodgers and the Angels:
\[
b = 57
\]

### Step 3: Finding \( c \)
We are given that 82 people support only the Angels:
\[
c = 82
\]

### Step 4: Finding \( a \)
The total number of people who do not support the Angels is 301. This includes people who support only the Dodgers and people who do not support either team:
\[
a + d = 301
\]
Since \( d = 220 \), we can substitute and solve for \( a \):
\[
a + 220 = 301
\]
\[
a = 301 - 220 = 81
\]

### Summary of Results:
- \( a \) = 81 (people who support only the Dodgers)
- \( b \) = 57 (people who support both the Dodgers and the Angels)
- \( c \) = 82 (people who support only the Angels)
- \( d \) = 220 (people who do not support either team)

Would you like more details on how these were calculated, or do you have any other questions?

Here are 5 related questions to consider:
1. How can Venn diagrams visually represent the data?
2. What percentage of people support only the Dodgers?
3. What percentage of people support at least one of the two teams?
4. How many people support the Dodgers but not the Angels?
5. What percentage of the people support neither team?

**Tip:** Venn diagrams are a great tool to visually organize overlapping groups in problems involving surveys or sets!

Explore how to analyze survey data about support for the Dodgers and Angels. Learn about set theory concepts such as exclusive and intersection sets. Includes step-by-step calculations to find the number of people supporting only the Dodgers, both teams, only the Angels, and those supporting neither team.

Math Problem Statement

Find a a, b b, c c, and d d. a

b

c

d

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