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Answer: Hi! Unfortunately, I couldn't find the answer on any other outside resources like Coursehero for example, but Brainly AI is an amazing tool for homework and explains the answers always in detail.
In a class of 40 students, the number of students who study French is 10 more than the number of students who study History. If 8 students study both French and History, we need to determine how many students study History and how many students study French.
To solve this problem, let's break it down step by step:
1. Let's assume the number of students who study History is x.
2. Since the number of students who study French is 10 more than the number of students who study History, the number of students who study French would be (x + 10).
3. We know that 8 students study both French and History.
4. To find the total number of students studying History, we add the number of students who study only History to the number of students who study both French and History. So the total number of students studying History is (x + 8).
5. To find the total number of students studying French, we add the number of students who study only French to the number of students who study both French and History. So the total number of students studying French is ((x + 10) + 8).
6. Since the total number of students in the class is 40, we can set up an equation: (x + 8) + ((x + 10) + 8) = 40.
7. Simplifying the equation, we get: 2x + 26 = 40.
8. Subtracting 26 from both sides, we get: 2x = 14.
9. Dividing both sides by 2, we get: x = 7.
Therefore, the number of students who study History is 7, and the number of students who study French is (7 + 10) = 17.
Step-by-step explanation: Hope this helps!!!
