document.write( "Question 293317: A survey of fruit tree growers showed the following:
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\n" ); document.write( "59 grew raspberries 23 grew both raspberries and blueberries
\n" ); document.write( "50 grew blueberries 11 grew both raspberries and strawberries
\n" ); document.write( "27 grew strawberries 14 grew both blueberries and strawberries
\n" ); document.write( "9 grew all three types 13 grew none of these three
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\n" ); document.write( "Create a Venn diagram to reflect the above data, label your diagram clearly and submit to the Week 2, assignment 3 dropbox. Use your diagram to answer the following questions here.
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\n" ); document.write( "(a) How many grew only blueberries?
\n" ); document.write( "(b) How many grew both raspberries and blueberries, but not strawberries?
\n" ); document.write( "(c) How many grew only raspberries?
\n" ); document.write( "(d) How many grew none of these three or only strawberries?
\n" ); document.write( "(e) How many fruit tree growers were surveyed? \n" ); document.write( "

Algebra.Com's Answer #211766 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "A survey of fruit tree growers showed the following:\r\n" );
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document.write( "59 grew raspberries     23 grew both raspberries and blueberries \r\n" );
document.write( "50 grew blueberries     11 grew both raspberries and strawberries\r\n" );
document.write( "27 grew strawberries    14 grew both blueberries and strawberries\r\n" );
document.write( "9 grew all three types       13 grew none of these three\r\n" );
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document.write( " \r\n" );
document.write( "Create a Venn diagram to reflect the above data, label your diagram clearly\r\n" );
document.write( "and submit to the Week 2, assignment 3 dropbox. Use your diagram to answer the following questions here.\r\n" );
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document.write( "(a)   How many grew only blueberries?\r\n" );
document.write( "(b)   How many grew both raspberries and blueberries, but not strawberries?\r\n" );
document.write( "(c)   How many grew only raspberries?\r\n" );
document.write( "(d)   How many grew none of these three or only strawberries?\r\n" );
document.write( "(e)   How many fruit tree growers were surveyed? \r\n" );
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document.write( "There are 8 types of growers here.\r\n" );
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document.write( "Grower       Growing       Growing          Growing  \r\n" );
document.write( "type       Raspberries   Blueberries      Strawberries \r\n" );
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document.write( "Type #1         YES           NO           NO\r\n" );
document.write( "Type #2         YES          YES           NO \r\n" );
document.write( "Type #3          NO          YES           NO  \r\n" );
document.write( "Type #4         YES           NO          YES \r\n" );
document.write( "Type #5         YES          YES          YES \r\n" );
document.write( "Type #6          NO          YES          YES\r\n" );
document.write( "Type #7          NO           NO          YES \r\n" );
document.write( "Type #8          NO           NO           NO\r\n" );
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document.write( "Let's draw three mutually overlapping circles:\r\n" );
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document.write( "Notice that there are 8 regions.\r\n" );
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document.write( "Regions #1, #2, #4, and #5 make up the set R, of raspberry growers.\r\n" );
document.write( "        \r\n" );
document.write( "       Region #1 consists only of those growing raspberries, but who are\r\n" );
document.write( "       NOT growing blueberries and NOT growing strawberries. \r\n" );
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document.write( "       Region #2 consists only of those growing BOTH raspberries and\r\n" );
document.write( "       blueberries, but who are NOT growing strawberries.\r\n" );
document.write( "       \r\n" );
document.write( "       Region #3 consists only of those growing blueberries, but who are\r\n" );
document.write( "       NOT growing raspberries and NOT growing strawberries.\r\n" );
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document.write( "       Region #4 consists only of those growing BOTH raspberries and\r\n" );
document.write( "       strawberries, but who are NOT growing blueberries.\r\n" );
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document.write( "       Region #5 consists only of those growing ALL THREE kinds of berries.  \r\n" );
document.write( "       \r\n" );
document.write( "       Region #6 consists only of those growing BOTH blueberries and\r\n" );
document.write( "       strawberries, but who are NOT growing raspberries.\r\n" );
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document.write( "       Region #7 consists only of those growing strawberries, but who are\r\n" );
document.write( "       NOT growing raspberries and NOT growing blueberries.\r\n" );
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document.write( "       Region #8 consists only of those NOT growing ANY of the  \r\n" );
document.write( "       kinds of berries.\r\n" );
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document.write( "Let's start with the most inclusive, i.e., those that grew some\r\n" );
document.write( "of all three types of berries:\r\n" );
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document.write( ">>...9 grew all three types...<<\r\n" );
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document.write( "That's the growers of type #5, so we erase #5 and put 9 in its place:\r\n" );
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document.write( " \r\n" );
document.write( ">>...23 grew both raspberries and blueberries...<<\r\n" );
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document.write( "Regions #2 and #5 grew raspberries and blueberries, and since region #5\r\n" );
document.write( "has 9 of the 23 already accounted for, the other 23-9 or 14 growers are in\r\n" );
document.write( "region #2, so erase #2 and put 14 in its place\r\n" );
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document.write( "           \r\n" );
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document.write( ">>...11 grew both raspberries and strawberries...<<\r\n" );
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document.write( "Regions #4 and #5 grew raspberries and strawberries, and since region #5\r\n" );
document.write( "has 9 of the 11 already accounted for, the other 11-9 or 2 growers are in\r\n" );
document.write( "region #4, so erase #4 and put 2 in its place\r\n" );
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document.write( "\r\n" );
document.write( ">>...14 grew both blueberries and strawberries...<<\r\n" );
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document.write( "Regions #5 and #6 grew blueberries and strawberries, and since region #5\r\n" );
document.write( "has 9 of the 14 already accounted for, the other 14-9 or 5 growers are in\r\n" );
document.write( "region #6, so erase #6 and put 5 in its place\r\n" );
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document.write( ">>...59 grew raspberries...<<\r\n" );
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document.write( "Regions #1, #2, #5, and #4 grew raspberries, and regions #2, #5, and #4\r\n" );
document.write( "have respectively 14, 9 and 2 of the 59 already accounted for, so we\r\n" );
document.write( "add 14+9+2 and get 25 of the 59 already accouted for, that leaves\r\n" );
document.write( "59-25 or 34 in region #1, so erase #1 and put 34 in its place\r\n" );
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document.write( "\r\n" );
document.write( ">>...50 grew blueberries...<<\r\n" );
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document.write( "Regions #2, #3, #5, and #6 grew raspberries, and regions #2, #5, and #6\r\n" );
document.write( "have respectively 14, 9 and 5 of the 50 already accounted for, so we\r\n" );
document.write( "add 14+9+5 and get 28 of the 50 already accouted for, that leaves\r\n" );
document.write( "50-28 or 22 in region #3, so erase #3 and put 22 in its place\r\n" );
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document.write( ">>...27 grew strawberries...<<\r\n" );
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document.write( "Regions #4, #5, #6, and #7 grew strawberries, and regions #4, #5, and #6\r\n" );
document.write( "have respectively 2, 9 and 5 of the 27 already accounted for, so we\r\n" );
document.write( "add 2+9+5 and get 16 of the 27 already accouted for, that leaves\r\n" );
document.write( "27-16 or 11 in region #7, so erase #7 and put 11 in its place\r\n" );
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document.write( ">>...13 grew none of these three...<<\r\n" );
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document.write( "These 13 are all in region #8, so erase #8 and put 13 in its place\r\n" );
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document.write( "(a)   How many grew only blueberries?\r\n" );
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document.write( "These are in region #3, so the answer is 22\r\n" );
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document.write( "(b)   How many grew both raspberries and blueberries, but not strawberries?\r\n" );
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document.write( "These are in regions #2 and #5, so the answer is 14+9 or 23\r\n" );
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document.write( "(c)   How many grew only raspberries?\r\n" );
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document.write( "These are in region #1, so the answer is 34\r\n" );
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document.write( "(d)   How many grew none of these three or only strawberries?\r\n" );
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document.write( "These are in regions #8 and #1, do the answer is 13+34 or 47. \r\n" );
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document.write( "(e)   How many fruit tree growers were surveyed?\r\n" );
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document.write( "We add the numbers is all the eight regions:\r\n" );
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document.write( "34 + 14 + 22 + 2 + 9 + 5 + 11 + 13 = 110.\r\n" );
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document.write( "Edwin

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