In a class of 40 students the number of students who studies French is 10 more than the number of students who studies history. If 8 students study both French and history how many students study history and French

In a class of 40 students the number of students who studies French is 10 more than the number of students who studies history. If 8 students study both French and history how many students study history and French

make a Venn diagram of two intersecting circles, label them F and H

place 8 in the intersection of both.

Place a in the "French-only" part and b in the "history-only" part
then:
a + 8 + b = 40 ===> a+b = 32
a+8 - (b+8) = 10 ==> a-b = 10
add them
2a = 42
a = 21, and then b = 11
So 21+8 or 29 study French, and 11+8 or 19 study History

oops sorry its not wrong thing

To find out how many students study both History and French, we first need to determine the number of students who study each subject separately.

Let's assume the number of students who study History is x. According to the given information, the number of students who study French is 10 more than the number of students who study History. So, the number of students who study French would be (x + 10).

Since we know that 8 students study both French and History, we can set up an equation using the principle of inclusion-exclusion:

Total students studying History + Total students studying French - Total students studying both = Total number of students

In equation form:
(x) + (x + 10) - 8 = 40

Simplifying the equation:
2x + 2 = 48
2x = 48 - 2
2x = 46
x = 23

So, the number of students who study History is 23, and the number of students who study French is (23 + 10 = 33).

Therefore, the number of students who study both History and French is 8.

It is 17