
Did you sketch your Venn diagram?
The missing part is the intersection of all 3, label it x
Now look at the intersection of A and C, it must be 34.
But you already have x accounted for in the intersection of all 3.
So label the part in A and C, but not B as 34x
36 study A and B, so the part of A and B, but not C is
36x
Given that 53 study Art, in the A only part we can put
53(36x)  (34x) x = x  17
6 study B only, put that in.
So the missing part of B is 60  6  (36x)  x
= 18
18 study B , but not C, so they could be in A
label the part of A and B, but not C as 18
BUT, we already know that A and B, not C, is 36x
So 36x = 18
X=18
I think we are done
Finish circle A, with A only as x17 or 1817 = 1
Replace the other values.
We still are missing the C only part.
But we know that the total of all the parts is 80
By simple subtraction, the C only part is 3
Check by verifying each part with the given information.
Arts only is 1
Chemistry is 55

Mr Kwame's mistake was the place to find the value of x.
Biology but not chemistry means that, biology only plus the intersection of biology and Art.
So it should have been 6 +36x=18. It means x=24.
So the value of all the intersections of the regions is 24.
Finishing circle A, with A only as x17 or 2417 = 7.
Let q denote the intersection of biology and chemistry only.
So 60(36x +x+6)= q.
> 60(3624+24+6)=q
= 6042=q
Therefore q = 18. Get it ?
We are still missing the C only part.
But we know that the total of all the parts is 80.
So to calculate for only C part,
80 (10+7+12+24+6+18)=y(i.e C only).
>8077=y
So y= 3. Thus only C is 3.
Those who study chemistry = 10+24+18+3=55.
From our working:
Arts only is 7 and
Chemistry is 55.
So akiola answer is correct.
I could have given you the venn diagram but I am using mobile device so I cannot give you the venn diagram.

Solution

what will be both chemistry and biology?

I want diagram

Please I need a venn diagram for this question

Art only should be 7 but not 1.

Correct!!!

1 and 55

art only should be 7 and chemistry is 55 according to akiola from answers given

Sorry, Mr. Reiny rather not Mr. Kwame.Trial; In a class of 70 students, 6 offer Economics only, 18 offer Economics but not Mathematics, 36 offer Economics and Geography, 53 offer Economics, 50 offer Geography and 34 offer Mathematics and Geography. All students offer at least one subject. Determine the number of students who offer: (1)mathematics (2)mathematics and geography but not economics.

Thanks for letting me understand

Excellent work

Very educative.

I am yet to u understand

Thanks senior

Arts only = 1
Chemistry = 55
Both biology and chemistry is 0