In a class of 80 students,53 study Art,60 study Biology,36 study biology and Art,34 study Art and chemistry and 6 study Biology only
a.Illastrate the information on a Venn diagram
b.Determin the number of the students who study
I.Art only
ii.Chemistry
4 answers
I don't know please help me
Please help me
Paste your question in google.
When you see list of result go on:
g a u t h m a t h . c o m › algebra › set theory
26. In a class of 80 students, 53 study Art, 60 st - Gauthmath
You will see solution and explanation.
When you see list of result go on:
g a u t h m a t h . c o m › algebra › set theory
26. In a class of 80 students, 53 study Art, 60 st - Gauthmath
You will see solution and explanation.
sketch 3 intersecting circles, label them A, B, C
We don't know how many take all 3, so label the inner intersection as x
36 go into B and A, but we have already accounted for x of those,
so label the "B and A only" as 36-x, similarly
label the "A and C only" as 34-x
enter 6 in the "B only"
Now look at the B circle, we are missing the "B and C only" , call it y
then y + 6 + 36-x + x = 60
y = 18 , enter 18 in the "B and C only" section
Back to the A circle, we know the total is 53, and we don't know the "A only"
call it z
z + 36-x + x + 34-x = 53
z = x - 17
The only part not filled in is the "C only" , let's call that c
We know the total of all the entries should be 80, assuming that everbody
takes at least one of the subjects.
all of A + 6+18 + c = 80
53 + 6 + 18 + c = 80
c = 3 , fill that in
We have now filled in all the sections, but still don't know what x is
the only thing we know about x is that
17 < x < 34 , for x to be positive
We do know that C contains a total of 55
If we pick any value of x within the domain above, the Venn diagram entries
will be consistent, try it with x = 20, it will work out
Did you miss some additional data? e.g. did you know how many
took all 3 ??
We don't know how many take all 3, so label the inner intersection as x
36 go into B and A, but we have already accounted for x of those,
so label the "B and A only" as 36-x, similarly
label the "A and C only" as 34-x
enter 6 in the "B only"
Now look at the B circle, we are missing the "B and C only" , call it y
then y + 6 + 36-x + x = 60
y = 18 , enter 18 in the "B and C only" section
Back to the A circle, we know the total is 53, and we don't know the "A only"
call it z
z + 36-x + x + 34-x = 53
z = x - 17
The only part not filled in is the "C only" , let's call that c
We know the total of all the entries should be 80, assuming that everbody
takes at least one of the subjects.
all of A + 6+18 + c = 80
53 + 6 + 18 + c = 80
c = 3 , fill that in
We have now filled in all the sections, but still don't know what x is
the only thing we know about x is that
17 < x < 34 , for x to be positive
We do know that C contains a total of 55
If we pick any value of x within the domain above, the Venn diagram entries
will be consistent, try it with x = 20, it will work out
Did you miss some additional data? e.g. did you know how many
took all 3 ??