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solve the following problem by representing it in a venn diagram at a children s party the children are asked their prefer

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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?

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Dexter

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114 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

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