document.write( "Question 1135719: Out of the 95 travellers interviewed, 7 travelled by bus and train only, 3
\n" ); document.write( "by train and car only and 8 travelled by all three means of transport. The
\n" ); document.write( "number, x, of travellers who travelled by bus only equal to the number who
\n" ); document.write( "travelled by bus and car only. If 47 people travelled by bus and 30 by
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\n" ); document.write( "(i) represent this information in a Venn diagram;
\n" ); document.write( "(ii) calculate the
\n" ); document.write( " I. value of x;
\n" ); document.write( " II. number who travelled by at least two means. \n" ); document.write( "

Algebra.Com's Answer #753387 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
Out of the 95 travellers interviewed, 7 travelled by bus and train only, 3
\n" ); document.write( "by train and car only and 8 travelled by all three means of transport. The
\n" ); document.write( "number, x, of travellers who travelled by bus only equal to the number who
\n" ); document.write( "travelled by bus and car only. If 47 people travelled by bus and 30 by
\n" ); document.write( "train.
\n" ); document.write( "(i) represent this information in a Venn diagram;\r
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document.write( "Here is how I got the Venn diagram above:\r\n" );
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document.write( "All the train travelers are inside the red circle.\r\n" );
document.write( "All the bus travelers are inside the blue circle.\r\n" );
document.write( "All the car travelers are inside the green circle.\r\n" );
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>>>7 travelled by bus and train only,....<<<

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document.write( "So put 7 in the region that is in the red and blue circles but not in\r\n" );
document.write( "the green circle.\r\n" );
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>>>3 by train and car only...<<<

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document.write( "So put 3 in the region that is in the red and green circles but not in\r\n" );
document.write( "the blue circle.\r\n" );
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>>>and 8 travelled by all three means of transport....<<<

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document.write( "So put 8 in the middle region that is in all three circles.\r\n" );
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>>>The number, x, of travellers who travelled by bus only....<<<

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document.write( "So put x in the region that is in the blue circle but not in either\r\n" );
document.write( "of the other two circles.\r\n" );
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>>>equals to the number who travelled by bus and car only....<<<

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document.write( "So also put x in the region that is in the blue and green circles but not in\r\n" );
document.write( "the red circle. \r\n" );
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document.write( "No mention has been made of the train travelers only, so we put\r\n" );
document.write( "y in the region that is only in the red circle and not in either\r\n" );
document.write( "of the other circles.\r\n" );
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document.write( "No mention has been made of the car travelers only, so we put\r\n" );
document.write( "z in the region that is only in the green circle and not in either\r\n" );
document.write( "of the other circles.\r\n" );
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>>>If 47 people travelled by bus...<<<

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document.write( "So we add everything inside the blue circle and set the sum\r\n" );
document.write( "equal to 47\r\n" );
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document.write( "7+8+x+x = 47\r\n" );
document.write( "  15+2x = 47\r\n" );
document.write( "     2x = 32\r\n" );
document.write( "      x = 16\r\n" );
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>>>and 30 by train....<<<

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document.write( "So we add everything inside the red circle and set the sum\r\n" );
document.write( "equal to 30\r\n" );
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document.write( "y+7+3+8 = 30\r\n" );
document.write( "   y+18 = 30\r\n" );
document.write( "      y = 12\r\n" );
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document.write( "We only need find z.  We use the very first clause:\r\n" );
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>>>Out of the 95 travellers interviewed,...<<<

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document.write( "We add all the numbers in all the regions and set the sum\r\n" );
document.write( "equal to 95\r\n" );
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document.write( "y+7+8+3+x+x+z = 95\r\n" );
document.write( "    y+18+2x+z = 95\r\n" );
document.write( "12+18+2(16)+z = 95\r\n" );
document.write( "      30+32+z = 95\r\n" );
document.write( "         62+z = 95\r\n" );
document.write( "            z = 33\r\n" );
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document.write( "Putting all the values we have calculated in the Venn diagram:\r\n" );
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document.write( "

>>>(ii) calculate the
\n" ); document.write( " I. value of x;...<<<

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document.write( "We found x to be 16\r\n" );
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>>>II. number who travelled by at least two means...<<<

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document.write( "That's the sum of the number in the regions that are part\r\n" );
document.write( "of two circles or all three circles, so we add those four \r\n" );
document.write( "regions:\r\n" );
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document.write( "7+8+3+16 = 34\r\n" );
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document.write( "Edwin

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