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 8students study both french and history, History. How many students study I. French ii. History
If everyone studies something, then if x study history, you have
x + x+10 - 8 = 40
two set problem
To find the number of students studying French and History, we need to use some basic concepts of set theory. Let's break down the information given step by step.
We know that the total number of students in the class is 40. Let's represent this with the symbol N.
Let's assume the number of students studying History is H and the number of students studying French is F.
We are given two pieces of information:
1. The number of students studying French is 10 more than the number of students studying History.
This can be expressed as: F = H + 10.
2. 8 students study both French and History.
This means that there is an intersection between the sets of students studying French and History, and the number of students studying both is 8.
To solve this problem, we can use the principle of inclusion-exclusion.
Total students studying French or History (F ∪ H) can be obtained by adding the number of students studying French (F) to the number of students studying History (H) and then subtracting the intersection (F ∩ H).
So, N(F ∪ H) = N(F) + N(H) - N(F ∩ H)
or
40 = F + H - 8.
We can simplify this equation using the value we found earlier, F = H + 10.
40 = H + 10 + H - 8
40 = 2H + 2.
Now, we can solve this equation for H.
Subtracting 2 from both sides:
40 - 2 = 2H
38 = 2H.
Dividing both sides by 2:
H = 19.
Therefore, the number of students studying History is 19.
To find the number of students studying French, we can substitute the value of H into the equation F = H + 10:
F = 19 + 10
F = 29.
Therefore, the number of students studying French is 29.
So, in summary:
i. The number of students studying French is 29.
ii. The number of students studying History is 19.