Question 1034484: In a village , out of 120 farmers, 93 farmers have grown vegetables, 63 have grown flowers, 45 have grown sugarcane, 45 farmers have grown vegetables and flowers, 24 farmers have grown flowers and sugarcane, 27 farmers have grown vegetables and sugarcane. Find the number of farmers who have grown vegetables, flowers and sugarcane using venn diagram only.(not by using formulas)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the venn diagram will have 3 circles that intersect.
the first circle is vegetables.
the second circle is fruit.
the third circle is sugar cane.
the following letters will be used to represent each part of the venn diagram.
v = vegetabls circle.
f = fruit circle.
s = sugar cane circle.
u = universe rectangle.
there will be 4 intersections.
one intersection is between vegetables and fruit.
one intersection is between vegetables and sugar cane.
one intersection is between fruit and sugar cane.
one intersection is between vegetables and fruit and sugar cane.
the vegetable circle will contain the intersection between vegetables and fruit, vegetables and sugar cane, and all three.
the fruit circle will contain the intersection between fruit and vegetables, fruit and sugar cane, and all three.
the sugar cane circle will contain the intersection between sugar cane and vegetables, sugar cane and fruit, and all three.
there will be 4 parts to each circle.
the parts of the vegetable circle will be:
vegetable only.
vegetable and fruit.
vegetable and sugar cane.
vegetable and fruit and sugar cane.
the parts of the fruit circle will be:
fruit only.
fruit and vegetable.
fruit and sugar cane.
fruit and vegetable and sugar cane.
the parts of the sugar cane circle will be:
sugar cane only.
sugar cane and vegetable.
sugar cane and fruit.
sugar cane and vegetable and fruit.
you are given:
the vegetable circle contains 93, 45 of which are in the vegetable and fruit part, and 27 of which are in the vegetable and sugar cane part.
the fruit circle contains 63, 45 of which are in the fruit and vegetable part, and 24 of which are in the fruit and sugar cane part.
the sugar cane circle contains 45, 27 of which are in the sugar cane and vegetable part, and 24 of which are in the sugar cane and fruit part.
you are not given the vegetable and fruit and sugar cane part.
this is what you need to find.
some logic is required.
otherwise you won't be able to solve this correctly.
the logic is:
the amount that is in the vegetable and fruit and sugar cane part will have to be subtracted from the vegetable and fruit part, from the vegetable and sugar cane part, and from the fruit and sugar cane part.
the reason is that the vegetable and fruit and sugar cane part is included in the numbers for those other parts.
once you have done that, then you can follow the logic and solve the problem.
we let x = the vegetable and fruit and sugar cane part.
since that has to be subtracted from the vegetable and fruit part, then the vegetable and fruit part becomes 45 - x.
since that has to be subtracted from the vegetable and sugar cane part, then the vegetable and sugar cane part becomes 27 - x.
since that has to be subtracted from the fruit and sugar cane part, then the fruit and sugar cane part becomes 24 - x.
your venn diagram will look like this before you do any calculations.
the calculations will look like this:
your venn diagram will look like this after you do the calculations.
the venn diagram requires the logic to be applied before you can complete it with all the parts having their specific values assigned.
since the intersection of all 3 is equal to 15, then:
45 - 15 = 30
27 - 15 = 12
24 - 15 = 9
this give you the net value for the intersection of every 2 of the circles.
93 - 30 - 12 - 15 = 36
63 - 30 - 9 - 15 = 9
45 - 12 - 9 - 15 = 9
the venn diagram is complete.
the vegetable circle is composed of:
36 vegetable only.
30 vegetable and fruit.
12 vegetable and sugar cane.
15 vegetable and fruit and sugar cane.
total = 93.
similar calculations are done for each of the other 2 circles.
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