document.write( "Question 148876: a survey of a school 0f 850 students found that 150 used a bus to get to school, 75 used a train and 650 user neither. using a venn diagram, calculate the number of students who used both a bus and a train to get to school. \n" ); document.write( "

Algebra.Com's Answer #109230 by Edwin McCravy(20056) $\"\"$ $\"About$

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a survey of a school 0f 850 students found that 150 used a bus to get to school, 75 used a train and 650 user neither. using a venn diagram, calculate the number of students who used both a bus and a train to get to school.
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document.write( "Imagine you have all 850 students in the bleachers of football field.\r\n" );
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document.write( "First draw a big rectangle to represent, say, a big football field, for\r\n" );
document.write( "all 850 students to come down and stand in.\r\n" );
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document.write( "Now on that football field draw a big circle for all 150 students\r\n" );
document.write( "to stand in who used a bus and label it B:\r\n" );
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document.write( "Next draw another big circle overlapping it for all 75 students\r\n" );
document.write( "to stand in who used a train and label it T:\r\n" );
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document.write( "Now the 650 students who use neither bus nor train will have to stand\r\n" );
document.write( "on the field outside both circles, so we'll write 650 out there to\r\n" );
document.write( "stand for the 650 students who will stand out there:\r\n" );
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document.write( "We need to know how many people will be standing in both circles, \r\n" );
document.write( "that is, how many will be standing in this overapping part of the \r\n" );
document.write( "two circles:\r\n" );
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document.write( "`                 \r\n" );
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document.write( "So we'll let  represent the number of students in that region,\r\n" );
document.write( "so we'll write \"x\" in there:\r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Since there are 150 students who used a bus, the rest of those 150 \r\n" );
document.write( "besides the x that used both, that is, 150-x, will have to stand in \r\n" );
document.write( "this region, in which we write 150-x:\r\n" );
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document.write( "  \r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "---\r\n" );
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document.write( "Since there are 75 students who used a train, the rest of those 75 \r\n" );
document.write( "besides the x that used both, that is, 75-x, will have to stand in \r\n" );
document.write( "this region, in which we write 75-x:\r\n" );
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document.write( "`                      `  \r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Now we add up all the numbers in the four regions and\r\n" );
document.write( "that sum must equal the entire 850 students standing somewhere\r\n" );
document.write( "on the football field:\r\n" );
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document.write( "Solve that and get \r\n" );
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document.write( "The answer is 25 students used both bus and train.\r\n" );
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document.write( "----\r\n" );
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document.write( "If you didn't have to use a Venn diagram, you could have\r\n" );
document.write( "done it easier with this formula:\r\n" );
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document.write( "N(B or T) = N(B) + N(T) - N(B and T)\r\n" );
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document.write( "850-650 = 150 + 75 - N(B and T)\r\n" );
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document.write( "200 = 225 - N(B and T)\r\n" );
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document.write( "N(B and T) = 225 - 200\r\n" );
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document.write( "N(N and T) = 25.\r\n" );
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document.write( "Edwin

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