In a class of 40 student,the number of student who study french is 10 more than the number of student who study history.if 8 student study both french and history,how many student study (1)history (2) french
french alone = f
history alone = h
both = 8
f+8 - 10 = h+8
or
f-h = 8
and
f+h + 8 = 40
or f+h = 32
so
2f =40
f = 20
h = 12
so
f+8 = 28 study french or both
h+8 = 20 study history or both
french alone = f
history alone = h
both = 8
f+8 - 10 = h+8
or
f-h = 10
and
f+h + 8 = 40
or f+h = 32
so
2f =42
f = 21
h = 11
so
f+8 = 29 study french or both
h+8 = 19 study history or both
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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 with both french and history, how many students study (i) french (ii) history
In a class 40 student the number of student who study french is 10 more than the number of student who study history.if 8 student study both french and history.how many student study history and french.
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In a class of40 students, the number of students who study French is 10 more than the of students ho study History. if 8 students study both French and History. how many students study:I History ii French solve it with solution and show working
Yes
To find the number of students studying history and French, we can solve this problem using the principle of inclusion-exclusion.
Let's denote:
H = Number of students studying history
F = Number of students studying French
We are given the following information:
Total number of students = 40
Number of students studying both French and history = 8
From the given information, we can deduce two equations:
1. The number of students studying French is 10 more than the number of students studying history:
F = H + 10 --------(Equation 1)
2. The total number of students studying either French or history is 40:
F + H - 8 = 40 --------(Equation 2)
(Here, we subtract 8 since these students were counted twice when we consider students studying both French and history.)
Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of H and F.
Let's solve them:
Substitute the value of F from Equation 1 into Equation 2:
(H + 10) + H - 8 = 40
2H + 2 = 40
2H = 40 - 2
2H = 38
H = 38/2
H = 19
Substitute the value of H = 19 into Equation 1 to find F:
F = H + 10
F = 19 + 10
F = 29
Therefore, the number of students studying:
(1) History = 19
(2) French = 29