Question 308815: A survey of fruit tree growers showed the following:
71 grew raspberries 25 grew both raspberries and blueberries
46 grew blueberries 16 grew both raspberries and strawberries
31 grew strawberries 20 grew both blueberries and strawberries
11 grew all three types 7 grew none of these three
(a) How many grew only raspberries?
(b) How many grew only strawberries?
(c) How many grew both strawberries and raspberries, but not blueberries?
(d) How many grew exactly two of these three?
(e) How many fruit tree growers were surveyed?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Draw a big rectangle with three circles inside that overlap each other, like this
The rectangle is the Universe -- a container for all of the growers that were surveyed. Each of the circles is a container for one of the three types of fruit, and they are labeled R, B, and S for raspberries, blueberries, and strawberries. By the way, it is extremely odd that someone would be surveying fruit TREE growers about these three fruits in light of the fact that none of these fruits grow on trees.
Now the last thing we are told is that 11 of the growers grow all three fruits and 7 of the growers surveyed grew none of them. So put an 11 in the center space where the three circles overlap and put a 7 outside of the three circles but still inside the rectangle.
Now we also know that 20 grew both blueberries and strawberries. However, the 11 that grew all three ALSO grew both blueberries and strawberries, hence 20 minus 11 = 9 ONLY grew blueberries and strawberries. Write a 9 in the space where the B and S circles overlap. Likewise, 16 - 11 = 5 is the number that only grew raspberries and strawberries, and 25 - 11 = 14 is the number that only grew raspberries and blueberries. Put those numbers in their spaces as well.
Next we know that 71 grew raspberries, but 14 + 11 + 5 = 30 of those grew something else as well, so 71 minus 30 equals 41. Enter the 41.
You should have the pattern figured out by now, so I'll let you fill in the other two numbers. The sum of all the numbers on the diagram answers the last question. The other answers are readily available from the filled in diagram.
John
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