Pregunta
10. In a class of 80 students, every student studies Mathematics or Geography or both. If 65 students study Mathematics and 50 study Geography, how many study both subjects?
Ask by Mills Newton. in Nigeria
Jan 30,2025
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35 students study both Mathematics and Geography.
Solución
To determine the number of students who study both Mathematics and Geography, we can use the **principle of inclusion-exclusion**.
**Given:**
- Total number of students = 80
- Students studying Mathematics (M) = 65
- Students studying Geography (G) = 50
**Objective:**
Find the number of students studying both Mathematics and Geography (M ∩ G).
**Using the Inclusion-Exclusion Principle:**
\[
|M \cup G| = |M| + |G| - |M \cap G|
\]
Since every student studies Mathematics or Geography or both:
\[
|M \cup G| = 80
\]
Plugging in the values:
\[
80 = 65 + 50 - |M \cap G|
\]
\[
80 = 115 - |M \cap G|
\]
Solving for \(|M \cap G|\):
\[
|M \cap G| = 115 - 80 = 35
\]
**Answer:**
35 students study both Mathematics and Geography.
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Simplifique esta solución Beyond the Answer
To find the number of students studying both subjects, we can use the formula for the union of two sets. Let M be the number of students studying Mathematics, G for Geography, and B for both subjects. According to the principle of inclusion-exclusion: Total = M + G - B We know the total number of students is 80, M = 65, and G = 50. Plugging these values into the equation gives us: 80 = 65 + 50 - B Simplifying this: 80 = 115 - B B = 115 - 80 B = 35 So, the number of students studying both subjects is 35!
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