Problem

In a class of 35 students, 16 were History majors, 7 were English majors, and 3 were dual majors in History and English. How many students were majoring in History or English (or both)?

Answer

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Answer

Final Answer: The total number of students majoring in History or English (or both) is \(\boxed{20}\).

Steps

Step 1 :Let's denote the number of History majors as \(H\), the number of English majors as \(E\), and the number of dual majors as \(D\).

Step 2 :Given that \(H = 16\), \(E = 7\), and \(D = 3\).

Step 3 :We need to find the total number of students majoring in History or English. This can be found by adding the number of History majors and English majors. However, since the dual majors are counted in both the History and English majors, we are double counting them. So, we need to subtract the number of dual majors from the total.

Step 4 :So, the total number of students majoring in History or English (or both) is \(H + E - D\).

Step 5 :Substituting the given values, we get \(16 + 7 - 3 = 20\).

Step 6 :Final Answer: The total number of students majoring in History or English (or both) is \(\boxed{20}\).

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