SOLUTION: A group of market women sell at least one of the following items of food stuffs. Yam,corn,and plantain.18 of them sell corn,17 sell yam and 19 sell plantain.8 sell plantain and cor

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Question 1205709: A group of market women sell at least one of the following items of food stuffs. Yam,corn,and plantain.18 of them sell corn,17 sell yam and 19 sell plantain.8 sell plantain and corn and 12 sell yam and plantain and 5 sell all the food stuffs.Draw a venn diagram to illustrate the information above.Find the total number of women in the group.Find the total number of women who sell one of the food stuffs.
Found 3 solutions by ikleyn, math_tutor2020, MathTherapy:
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

In this post, some key information is missed / lost,
making the solution INPOSSIBLE.

Double check your post comparing it with the source.


If you will find your fault, re-post your update to the forum.

Please do not post your update to me in person.



Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

As it stands right now, this question is incomplete. It is missing 1 key detail. I'll try my best to explain.

Draw 3 partially overlapping circles with these labels
Y = yam
C = corn
P = plantain

Letters 'a' through 'h' indicate the following
a = yams only
b = yams and corn only (but no plantains)
c = corn only
d = yams and plaintains only (but no corn)
e = all 3 items mentioned
f = corn and plaintains only (but no yams)
g = plantains only
h = none of the 3 items mentioned

Here's the given info
NumberStatement
Fact 1A group of market women sell at least one of the following items of food stuffs. Yam,corn,and plantain.
Fact 218 of them sell corn
Fact 317 sell yam
Fact 419 sell plantain
Fact 58 sell plantain and corn
Fact 612 sell yam and plantain
Fact 75 sell all the food stuffs


fact 1 means that h = 0.

fact 7 leads to e = 5.

Let's combine fact 6 and fact 7
12 sell yam and plantain. Five sell all three types, so 12-5 = 7
Therefore, d = 7


Combine fact 5 and fact 7 to determine that 8-5 = 3 women sell plantain and corn but no yams.
3 goes inside region f
f = 3

Here's what we found so far
d = 7
e = 5
f = 3
h = 0

Focus on circle P.

Fact 4 tells us that 19 women sell plantains (some sell other vegetables as well).
The items inside circle P must add to 19.
g+7+5+3 = 19
g+15 = 19
g = 19-15
g = 4
There are 4 women who sell plantains only.

Now focus on circle Y and fact 3
Because of this given fact, the items in this circle must add to 17.
a+b+7+5 = 17
a+b+12 = 17
a+b = 17-12
a+b = 5

Through similar logic (focus on circle C and fact 2), you'll find that b+c+5+3 = 18 leads to b+c = 10

We have this system of equations
a+b = 5
b+c = 10
It has 3 variables. Since there are more variables than equations, we do not have enough information to find the numeric value of a,b, nor c.
We need 3 equations to solve for 3 variables.
This is where we come up short.

The general rule for Venn Diagram problems is this: There are 8 regions ('a' through h) so we need 8 given facts of information.
Unfortunately we're only given 7 facts so we're one fact short.
The problem is incomplete.
Please make sure you didn't miss something to type in, or ask your teacher to see if s/he might have made a typo somewhere.

Refer to these similar Venn Diagram questions to see examples of 8 given facts to help fill out the Venn Diagram.
https://www.algebra.com/algebra/homework/Subset/Subset.faq.question.1204958.html
and
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1201924.html
and
https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1199899.html
and
https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.1199621.html
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
A group of market women sell at least one of the following items of food stuffs. Yam,corn,and plantain.18 of them sell corn,17 sell yam and 19 sell plantain.8 sell plantain and corn and 12 sell yam and plantain and 5 sell all the food stuffs.Draw a venn diagram to illustrate the information above.Find the total number of women in the group.Find the total number of women who sell one of the food stuffs.


Number of market women who sell "Yam, ONLY," "Corn, ONLY," or "Yam and Corn, ONLY" is needed to provide the answers!

The above diagram is the furthest one can take this "thing." In this diagram, number of women who sell yams, corn,
and plantains, are denoted by Y, C, and P, respectively.
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