Algebra.Com's Answer #92785 by Edwin McCravy(20060)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
Please show me how to solve this problem ( it was a homework problem (1 complete problem) and I didn't know where to start). thanks!
\n" );
document.write( "200 Students
\n" );
document.write( "70 Students take English class
\n" );
document.write( "54 Students take Math class
\n" );
document.write( "45 Students take Social Studies
\n" );
document.write( "28 Students take English and Math
\n" );
document.write( "19 Students take English and Scial Studies
\n" );
document.write( "15 Students take Math and Scial Studies
\n" );
document.write( "10 Students take English, Math and Social Studies
\n" );
document.write( "1.) How many students take English
\n" );
document.write( "2.) How many Students take math only
\n" );
document.write( "3.) How many Students take English, social studies but not math
\n" );
document.write( "4.) How many students take math and social studies but not English class
\n" );
document.write( "5.) How many do not take any class.\r
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( "Draw a big square to put all 200 students in:\r\n" );
document.write( " \r\n" );
document.write( "Now inside the square, draw a circle to put the\r\n" );
document.write( "70 English students in and label it E\r\n" );
document.write( " \r\n" );
document.write( "Now inside the rectangle, draw a second circle which\r\n" );
document.write( "overlaps the first circle to put the 54 Math stdents\r\n" );
document.write( "in. Label it M:\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Notice that the \"football\" shaped region where those two\r\n" );
document.write( "circles overlap is where we will put the 28 students who\r\n" );
document.write( "take English and Math.\r\n" );
document.write( "\r\n" );
document.write( "Now inside the square, draw a third circle which\r\n" );
document.write( "overlaps the other two circles to put the 45 Social\r\n" );
document.write( "Studies students in. Label it S:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "You will notice there are 8 regions formed within the\r\n" );
document.write( "square. I will number them I, II, III, IV, V,\r\n" );
document.write( "VI, VII, and VIII\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Let's go through the seven given statements and identify which\r\n" );
document.write( "regions they are talking about:\r\n" );
document.write( "\r\n" );
document.write( "#1. 70 Students take English class. These 70 students are in the\r\n" );
document.write( "E circle, which is made up of regions I,II,IV,and V.\r\n" );
document.write( "\r\n" );
document.write( "#2. 54 Students take Math class. These 54 students are in the\r\n" );
document.write( "M circle, which is made up of regions II,III,V,and VI. \r\n" );
document.write( "\r\n" );
document.write( "#3. 45 Students take Social Studies. These 45 students are in the\r\n" );
document.write( "S circle, which is made up of regions IV,V,VI,and VII.\r\n" );
document.write( "\r\n" );
document.write( "#4. 28 Students take English and Math. These 28 students are in the\r\n" );
document.write( "overlapping parts of circles E and M, which is made up of regions\r\n" );
document.write( "II and V.\r\n" );
document.write( "\r\n" );
document.write( "#5. 19 Students take English and Social Studies. These 19 students are \r\n" );
document.write( "in the overlapping parts of circles E and S, which is made up of regions\r\n" );
document.write( "IV and V.\r\n" );
document.write( "\r\n" );
document.write( "#6. 15 Students take Math and Social Studies. These 15 students are in the\r\n" );
document.write( "overlapping parts of circles M and S, which is made up of regions\r\n" );
document.write( "V and VI.\r\n" );
document.write( "\r\n" );
document.write( "#7. 10 Students take English, Math and Social Studies. These 10 students are\r\n" );
document.write( "in the region where all three circles overlap. This consists of only one\r\n" );
document.write( "region, namely region V. It's shaped like a triangle with curved sides.\r\n" );
document.write( "\r\n" );
document.write( "Now since we know how many students region V contains, namely 10, we will\r\n" );
document.write( "write 10 in region V.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( "Next we go back to #6. It tells us there are 15 students \r\n" );
document.write( "altogether in regions V and VI. So since there are 10\r\n" );
document.write( "students in region V, there have to be 15-10 or 5 students\r\n" );
document.write( "in region VI. So we write 5 in region VI.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( "Next we go back to #5. It tells us there are 19 students \r\n" );
document.write( "altogether in regions IV and V. So since there are 10\r\n" );
document.write( "students in region V, there have to be 19-10 or 9 students\r\n" );
document.write( "in region IV. So we write 9 in region IV.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Next we go back to #4. It tells us there are 28 students \r\n" );
document.write( "altogether in regions II and V. So since there are 10\r\n" );
document.write( "students in region V, there have to be 28-10 or 18 students\r\n" );
document.write( "in region II. So we write 18 in region II.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Next we go back to #3. It tells us there are 45 students \r\n" );
document.write( "altogether in regions IV, V, VI and VII. So since there are 9\r\n" );
document.write( "students in region IV, 10 in V, and 5 in VI, which amounts to\r\n" );
document.write( "9+10+5 or 24, so the leaves 45-24 or 21 for region VII. So\r\n" );
document.write( "we write 21 in region VII\r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Next we go back to #2. It tells us there are 54 students \r\n" );
document.write( "altogether in regions II, III, V and VI. So since there are 18\r\n" );
document.write( "students in region II, 10 in V, and 5 in VI, which amounts to\r\n" );
document.write( "18+10+5 or 33, so the leaves 54-33 or 21 for region III. So\r\n" );
document.write( "we write 21 in region III:\r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Next we go back to #1. It tells us there are 70 students \r\n" );
document.write( "altogether in regions I, II, IV and V. So since there are 18\r\n" );
document.write( "students in region II, 10 in V, and 9 in IV, which amounts to\r\n" );
document.write( "18+10+9 or 37, so the leaves 70-37 or 33 for region I. So\r\n" );
document.write( "we write 33 in region I:\r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "There is still one region we haven't yet found, that is\r\n" );
document.write( "the number of students in the region which is inside\r\n" );
document.write( "the big square, but outside all the circles. This is\r\n" );
document.write( "region VIII.\r\n" );
document.write( "\r\n" );
document.write( "Now tthere are respectively, 33, 18, 21, 9, 10, 5, and\r\n" );
document.write( "21 students in I, II, III, IV, V, VI, and VII. They\r\n" );
document.write( "account for 33+18+21+9+10+5+21 or 117 students. So that\r\n" );
document.write( "leaves 200-117 or 83 students in outer region VIII. So \r\n" );
document.write( "we write 83 in region VIII:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now that we know how many students are in each of the eight\r\n" );
document.write( "regions, we are ready to answer any questions.\r\n" );
document.write( "\r\n" );
document.write( "The first question is:\r\n" );
document.write( "\r\n" );
document.write( "1.) How many students take English only?\r\n" );
document.write( "\r\n" );
document.write( "That's the 33 students in region I.\r\n" );
document.write( "\r\n" );
document.write( "2.) How many Students take math only.\r\n" );
document.write( "\r\n" );
document.write( "That's the 21 in region III \r\n" );
document.write( "\r\n" );
document.write( "3.) How many Students take English, social studies but not math\r\n" );
document.write( "\r\n" );
document.write( "That's the 9 in region IV\r\n" );
document.write( "\r\n" );
document.write( "4.) How many students take math and social studies but not English class\r\n" );
document.write( "\r\n" );
document.write( "That's the 5 in region VI.\r\n" );
document.write( "\r\n" );
document.write( "5.) How many do not take any class.\r\n" );
document.write( "\r\n" );
document.write( "That's the 83 in the outer region VIII.\r\n" );
document.write( "\r\n" );
document.write( "Edwin \r
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |