In a class of 60 students,the number of students who passed biology is 6 more than the number who passed chemistry.Every student passed at least one of the two subjects and 8 students passed both subjects.How many students passed biology and chemistry.
Let 'u' be total students in the school, n(u)=60.
Let 'B' be number of biology, n(B)=?
Let 'C' be number of Chemistry,n(C)=?
Let n(B n C)=8.
Let 'x' be those who sturdy chemistry only
✓sketch the Venn diagram and show all the information in it.
That is:
Write n(B)=? On top of first set
Write n(C)=? On top of second set
Write '6' in the first set
Write 'x' in the second set
Write '8' as intersection
>Now add all the three regions and equate to the union.i.e
(6 + 8 + x)=60
14 + x =60
X=46
i. Number of biology= (6+8)=14
ii.Number of Chemistry=(8+x)=(8+46)=56
iii.Number of those who sturdy only one game=(6+x)=but x=46, so we have (6+46)=52.
Let prove if we have our answers correct
NB: Addition of the three regions should be equal to the union.
We have (6+8+x)=60, but x= 46,so we have (6+8+46)=60
60=60✓✓✓✓✓✓✓✓✓✓✓✓is correct
Let U = number of students in the class. =60
Let B = students who passed Biology. = ?
Let C = students who passed Chemistry.
Let B n C = 8
Let C = Any English alphabet, say x.
Then biology will be x + 6 since students who passed Biology is 6 more than the number who passed Chemistry.
Therefore (x +6) - 8 + 8 + x - 8 = 60
2x - 2 = 60
2x = 62
x = 31
Now, only Biology is (x + 6) - 8 =29, x = 31
Only Chemistry is (x - 8) = 23, since x is 31
B + B n C + C = U
29 + 8 + 23 = 60
I like the way the answer was presented and it made me understand it very easily
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Please number of chemistry= (8+x)=(8+46)=56
I think is 54 but not 56
Why didn't you draw the Venn diagram
Draw your Venn diagram. You can see that if x students passed chemistry, then
x + x+6 - 8 = 60