SOLUTION: Out of the 95 travellers interviewed, 7 travelled by bus and train only, 3 by train and car only and 8 travelled by all three means of transport. The number, x, of travellers who

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Question 1135719: Out of the 95 travellers interviewed, 7 travelled by bus and train only, 3
by train and car only and 8 travelled by all three means of transport. The
number, x, of travellers who travelled by bus only equal to the number who
travelled by bus and car only. If 47 people travelled by bus and 30 by
train.
(i) represent this information in a Venn diagram;
(ii) calculate the
I. value of x;
II. number who travelled by at least two means.
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
My Venn diagram shows:
(1)
+x+%2B+x+%2B+7+%2B+8+=+47+
+2x+%2B+15+=+47+
+2x+=+32+
+x+=+16+
(2)
Number who traveled by at least 2 means:
+x+%2B+8+%2B+7+%2B+3+=+x+%2B+18+
+x+%2B+18+=+16+%2B+18+
+x+%2B+18+=+34+
This is:
[ bus and car only ] and [ train and car only ]
and [ bus and train only ] and [ all three only ]

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Out of the 95 travellers interviewed, 7 travelled by bus and train only, 3
by train and car only and 8 travelled by all three means of transport. The
number, x, of travellers who travelled by bus only equal to the number who
travelled by bus and car only. If 47 people travelled by bus and 30 by
train.
(i) represent this information in a Venn diagram; 

Here is how I got the Venn diagram above:

All the train travelers are inside the red circle.
All the bus travelers are inside the blue circle.
All the car travelers are inside the green circle.
>>>7 travelled by bus and train only,....<<<
 

So put 7 in the region that is in the red and blue circles but not in
the green circle.
>>>3 by train and car only...<<<
 

So put 3 in the region that is in the red and green circles but not in
the blue circle.
>>>and 8 travelled by all three means of transport....<<<
 

So put 8 in the middle region that is in all three circles.
>>>The number, x, of travellers who travelled by bus only....<<<
 

So put x in the region that is in the blue circle but not in either
of the other two circles.
>>>equals to the number who travelled by bus and car only....<<<

So also put x in the region that is in the blue and green circles but not in
the red circle. 

No mention has been made of the train travelers only, so we put
y in the region that is only in the red circle and not in either
of the other circles.

No mention has been made of the car travelers only, so we put
z in the region that is only in the green circle and not in either
of the other circles.
>>>If 47 people travelled by bus...<<<
 

So we add everything inside the blue circle and set the sum
equal to 47

7+8+x+x = 47
  15+2x = 47
     2x = 32
      x = 16
>>>and 30 by train....<<<

So we add everything inside the red circle and set the sum
equal to 30

y+7+3+8 = 30
   y+18 = 30
      y = 12

We only need find z.  We use the very first clause:
>>>Out of the 95 travellers interviewed,...<<<

We add all the numbers in all the regions and set the sum
equal to 95

y+7+8+3+x+x+z = 95
    y+18+2x+z = 95
12+18+2(16)+z = 95
      30+32+z = 95
         62+z = 95
            z = 33

Putting all the values we have calculated in the Venn diagram:
>>>(ii) calculate the
I. value of x;...<<<

We found x to be 16
>>>II. number who travelled by at least two means...<<<

That's the sum of the number in the regions that are part
of two circles or all three circles, so we add those four 
regions:

7+8+3+16 = 34

Edwin