Question
Solve the following problem by representing it in a Venn diagram. At a children's party, the children are asked their preference regarding the flavor of ice cream, obtaining the following results: 9 want chocolate, vanilla and strawberry; 12 strawberry and vanilla, 13 chocolate and strawberry, 15 chocolate and vanilla, 18 strawberry, 26 vanilla, 29 chocolate, 8 other flavors. a) How many children were at the party? b) How many only want to try a single flavor? c) How many children do not want vanilla?
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Answer to a math question Solve the following problem by representing it in a Venn diagram. At a children's party, the children are asked their preference regarding the flavor of ice cream, obtaining the following results: 9 want chocolate, vanilla and strawberry; 12 strawberry and vanilla, 13 chocolate and strawberry, 15 chocolate and vanilla, 18 strawberry, 26 vanilla, 29 chocolate, 8 other flavors. a) How many children were at the party? b) How many only want to try a single flavor? c) How many children do not want vanilla?
Dexter
4.7114 Answers
1. Let:
A = \text{set of children who want chocolate}
B = \text{set of children who want vanilla}
C = \text{set of children who want strawberry}
2. Given:
|A \cup B \cup C| = 50
3. Use the principle of inclusion-exclusion for three sets:
|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|
4. Substitute the given values:
29 + 26 + 18 - 15 - 13 - 12 + 9 = 50
5. Therefore, the total number of children at the party is:
\text{a) } |A \cup B \cup C| = 50
6. To find the number of children who only want a single flavor, calculate:
|A \setminus (B \cup C)| = 50 - 40 = 10
|B \setminus (A \cup C)| = 24 - 14 = 2
|C \setminus (A \cup B)| = 12 - 4 = 8
7. Therefore, the number of children who only want to try a single flavor is:
\text{b) } 10 + 2 + 8 = 20
8. To find the number of children who do not want vanilla:
\text{c) } 50 - 26 = 24
2. Given:
3. Use the principle of inclusion-exclusion for three sets:
4. Substitute the given values:
5. Therefore, the total number of children at the party is:
6. To find the number of children who only want a single flavor, calculate:
7. Therefore, the number of children who only want to try a single flavor is:
8. To find the number of children who do not want vanilla:
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