Question 1011077: Draw Venn and show a calculation to solve. Jon has a lawn care business. He has been hired to cut 30 lawns, trim 27 lawns, and weed 26 gardens. He cuts and trims 14 of them, trims and weeds 7, cuts and weeds 4, and cuts, trims, and weeds 6. How many different customers does Jon have?
Thanks !
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's your venn diagram.
look below for further comments.
he has a total of 30 lawns to be cut, 27 lawns to be trimmed, and 26 lawns to be weeded.
out of the 30 lawns to be cut, 14 have to be trimmed as well, 4 have to be weeded as well, and 6 have to be weeded and trimmed as well.
that leaves 6 that only have to be cut.
out of the 27 lawns to be trimmed, 14 have to be cut as well, 2 have to be weeded as well, and 6 have to be cut and weeded as well.
that leaves 5 that only need to be trimmed.
out of the 26 lawns that need to be weeded, 4 need to be cut as well, 2 need to be trimmed as well, and 6 needed to be cut and trimmed as well.
that leaves 14 that only need to be weeded.
the question is how many different customers does jon have.
he has 6 customers that only needed their lawns to be cut.
he has 5 customers that only needed their lawns to be trimmed.
he has 14 customers that only needed their lawns to be weeded.
he has 14 customers that only needed their lawns to be cut and trimmed.
he has 4 customers that only needed their lawns to be cut and weeded.
he has 2 customers that only needed their lawns to be trimmed and weeded.
he has 6 customers that needed their lawns to be cut, trimmed, and weeded.
add them you get 51 customers total.
each one of these categories is now distinct, whereas before, the categories were a mix.
that's what the venn diagram shows you.
it shows you each of the categories that are now distinct which means that the category only includes what the title of the cateogory says is there.
before, the category of cut lawns includes several other categories as well.
the venn diagram splits out the categories so that they're each distinct.
all you have to do then is add up the totals within each category and that's the number of customers you have because each one of those categories represents customers that needed that alone.
each one of the circles tells you the categories of cut lawns, trimmed lawns, weeded lawns.
each one of the overlaps tells you the numbers that involve two of the categories or all three.
the 4 and the 2 in the middle involve two of the categories.
the 6 in the middle involves all three categories.
Answer by MathTherapy(10810)  (Show Source):
You can put this solution on YOUR website! Draw Venn and show a calculation to solve. Jon has a lawn care business. He has been hired to cut 30 lawns, trim 27 lawns, and weed 26 gardens. He cuts and trims 14 of them, trims and weeds 7, cuts and weeds 4, and cuts, trims, and weeds 6. How many different customers does Jon have?
Thanks !
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