in a class of 40 student study French or history. 20 student study both subject and the number of student who study French only is 10 more than the number who study history only and two study none of the subject. find; how many study French. how many study history
Yes
H + H+10 +20 = 40-2
H = 4 study history only
Now finish it off
To solve this problem, let's break it down step-by-step:
1. Let's assume the number of students who study French only is "F," and the number of students who study history only is "H."
- So, the number of students who study both French and history is 20.
- And the number of students who study none of the subjects is 2.
2. We know that the total number of students in the class is 40. So, we can write an equation using this information:
- F + H + 20 + 2 = 40
=> F + H + 22 = 40
3. Now, let's use another piece of information from the problem, which states that the number of students who study French only is 10 more than the number who study history only. We can represent this information as an equation:
- F = H + 10
4. Now, we can substitute the value of F from equation 3 into equation 2:
- (H + 10) + H + 22 = 40
=> 2H + 32 = 40
=> 2H = 8
=> H = 4
5. Plugging the value of H back into equation 3, we can find the value of F:
- F = 4 + 10
=> F = 14
Therefore, there are 14 students studying French, and 4 students studying history.
To solve this problem, we can use a Venn diagram. Let's assign variables to represent the number of students in each group.
Let's say:
F = number of students studying French only
H = number of students studying History only
B = number of students studying both French and History
N = number of students studying none of the subjects
From the given information, we can set up the following equations:
1) F + H + B + N = 40 (since there are 40 students in total)
2) B = 20 (as 20 students study both French and History)
3) F = H + 10 (as the number of students studying French only is 10 more than those studying History only)
4) N = 2 (as two students study none of the subjects)
Now, we can solve these equations to find the values of F and H.
Substitute equation (2) and equation (4) into equation (1):
(F + H + 20 + 2) = 40
F + H + 22 = 40
F + H = 18
Now substitute equation (3) into the equation (F + H = 18):
(H + 10 + H) = 18
2H + 10 = 18
2H = 18 - 10
2H = 8
H = 8/2
H = 4
Substitute the value of H into equation (3):
F = H + 10
F = 4 + 10
F = 14
Therefore, 14 students study French, and 4 students study History.