My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 14th, 2012, 04:27 AM   #1
Senior Member
 
Chikis's Avatar
 
Joined: Jan 2012

Posts: 739
Thanks: 7

Venn diagram

In a market
survey, 100
traders sell fruits.
40 sell apples, 46
oranges, 50
mangoes, 14
apples and oranges, 15 apples
and mangoes and
10 sell the three
fruits. Each of the
100 traders sells
atleast one of the
three fruits.
(i) Represent the
information in a
venn diagram.
(ii) Find the number
that sells oranges and mangoes only.

It difficult for me
to find the number
that sells oranges
and mangoes only.


I drew three circles
to show how the
traders sell the
fruits:

all the three fruits
n(AuOuM)
= 10

oranges n(O)
= 46-(4+10+x)
= 32

mangoes n(M).
= 50-(5+10+x)
= 35

apple n(A)
= 40-(4+10+5)
= 21

apples and oranges
n(AnO)
= 14-10
= 4

apples and
mangoes (AnM)
= 15-10
= 5

I don't know how
to find the number
of traders that
sells oranges and
mangoes only n
(OnM).
Please let n(OnM)
be x. What step or
direction of
thinking should I
take to find x ?
Chikis is offline  
 
October 14th, 2012, 07:34 AM   #2
Senior Member
 
Joined: Mar 2012
From: Belgium

Posts: 654
Thanks: 11

Re: Venn diagram


first of all where the ovals are overlapping 3 times you know its value is 10.

10 of the 15 people who sells apples and mangoes are selling the 3 fruits so there are 5 which are only selling apples and mangoes.

10 of the 14 people who sells apples and oranges are selling the 3 fruits so there are 4 which are only selling apples and mangoes.

10+4+5 of the 40 people who sells apples are selling something else then apples so there are 21 which are only selling apples.

there are in total 40+50+46-100=36 fruits which are sold in pairs. 10 of them are sold by 3 so we have to substract 10 of that 36=26.

4+5+10 of them aren't selling oranges and mangoes so there are 26-19=7 who do.
50-10-7-5=28 are selling mangoes only and 46-7-10-4=25 are selling oranges only.
gelatine1 is offline  
October 14th, 2012, 04:34 PM   #3
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Venn diagram

Hello, Chikis!

Quote:
In a market survey: 100 traders sell fruits.
[color=beige]. . [/color]40 sell apples,
[color=beige]. . [/color]46 sell oranges,
[color=beige]. . [/color]50 sell mangoes,
[color=beige]. . [/color]14 apples and oranges,
[color=beige]. . [/color]15 apples and mangoes
[color=beige]. . [/color]10 sell all three fruits.

Each of the 100 traders sells at least one of the three fruits.

(a) Represent the information in a Venn diagram.

(b) Find the number that sells oranges and mangoes only.

It looks like you were off to a good start.
Use the scroll bar to see the entire Venn diagram.

Code:
            *---------*  *---------* 
           /   Apples  \/  Oranges  \
          /            /\            \
         *      21    *  *   32-x     *
         |            | 4|            |
    [40] |        *---+--+---*        | [46]
         |       /    |10|    \       |
         *      /     *  *     \      *
          \    *   5   \/    x  *    /
           \   |       /\       |   /
            *--+--+---*  *------+--*
               |                |
               *      35-x      *
                \              /
                 \   Mangos   /
                  *----------*
                      [50]
Ten sold all three fruits.
The central intersection has "10".

15 sold apples and mangos.
Hence, there are 5 in the "apples and mangos only" region.

14 sold apples and oranges.
Hence, there are 4 in the "apples and oranges only" region.

The total in the Apples circle is 40.
[color=beige]. . [/color]Hence, "apples only" =


Let = number in "oranges and mangos only".

The total in the Mangos circle is 50.
[color=beige]. . [/color]Hence, "mangos only" = .

The total in the Oranges circle is 46.
[color=beige]. . [/color]Hence, "oranges only" =


If we add all the quantities in the diagram, we get
But we are told that this total is



soroban is offline  
October 15th, 2012, 07:04 AM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 20,472
Thanks: 2039

You don't need to be given the number of traders who sell all three fruits!
Let N denote the "number of traders who sell" function, then
40 + 46 + 50 = N(any fruit) + N(A and M) + N(A and O) + N(M and O only) = 100 + 15 + 14 + N(M and O only).
Hence N(M and O only) = 7.
skipjack is offline  
October 20th, 2012, 06:45 PM   #5
Senior Member
 
Chikis's Avatar
 
Joined: Jan 2012

Posts: 739
Thanks: 7

Re: Venn diagram

Thank you soroban!

Thanks to all of you; I have actually seen that:

(21+5+10+4)+(32-
x)+x (35-x) = 100
40+35-x+32-x+x = 100
-x = 100-107
x = -7/-1 = 7
Then the number trader x that sells
oranges and
mangoes will be 7.
Chikis is offline  
October 20th, 2012, 06:59 PM   #6
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 520

Math Focus: Calculus/ODEs
Re: Venn diagram

I have merged your duplicate topics together.

As you can see duplication of effort could have been prevented had you posted the topic only once. This is one reason we ask that you pick the most appropriate forum, then post your topic once. Not only does it prevent unnecessary duplication of effort from our valued contributors, who could be helping someone else instead of laboring to give help when the problem may already have been solved elsewhere, it prevents the cluttering of our forums with redundancy.
MarkFL is offline  
October 21st, 2012, 07:42 AM   #7
Senior Member
 
Chikis's Avatar
 
Joined: Jan 2012

Posts: 739
Thanks: 7

Re: Venn diagram

Am sorry for duplicating the post.
Chikis is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
diagram, venn



Search tags for this page
in a market survey 100traders sell fruits
,

apple orange mango venn diagram

,

In a market survey 100 traders sell fruits 40 sell apples, 46 oranges 50 mangos, 14 apples and orange 15 apples and mangos and 10 sell the three fruits each of the 100 traders sell at least one of the three fruits. Represent this on a venn diagram

,

in a market surcey 100 traders sells fruit, 40 sells apple, 46 sells oranges, 50 sells mangoes, 14 sells apples and oranges, 15 sells apples and mangoes, 10 sells the three fruit. find the number of people that sells oranges and mangoes

,

in a market survey a100 traders sells fruit

,

in a survey 100 sell fruits . 40 sell apples 46 sell orange 50 sell mangoes 14 sell apple and orange and 10 sell all the three fruits . each of the 100 traders at least sell at least one fruits

,

In a market survey,100 traders sells fruits ,40 sell Apples,46 Oranges,50 mangoes,14 Apples and Oranges,15 Apples and mangoes and 10 sell the three fruits.Each of the 100 traders sell at least one of the three fruits. (a) Represent the information in a ve

,

In a market survey,100 traders sells fruits ,40 sell Apples,46 Oranges,50 mangoes,14 Apples and Oranges,15 Apples and mangoes and 10 sell the three fruits.Each of the 100 traders sell at least one of the three fruits. (a) Represent the information in a ve

,

how hundred mangoes and 10 apples distributed to 50 people

,

apple orange mango diagram which relate this

,

How traders sells orange fruits on the street

,

in a market survey, 100 traders sell fruits, 46 sell apples, 4

,

In a market survey,100 traders sell fruit 40 sell apples,46 sell oranges,50 mangoes 14 sell apples and oranges,15 sell apple and mangoes and 10 sell the three fruit each of the 100 traders sell at least one of the three fruits.Represent the information on

,

in a market survey, 100 traders sell fruits, 40 sells apples,46 sell oranges,50 sell mangoes,14 sell both apple and oranges,15 sell both apple and mangoes, and 10 sell the three fruits, find the number that sells oranges and mangoes

,

in a market survey, 100 traders sell fruits, 40 sell apples, 46 oranges, 50 mangoes, 14 apples and oranges, 15 apples and mangoes, and 10 sell the three fruits. Each of the 100 traders sells at least one of the three fruits. (i) Represent the information

Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Help w/ Venn Diagram Criteria? JPArsenal87 Algebra 8 September 6th, 2013 07:20 AM
Venn Diagram equation help. MathsLOL Algebra 14 March 3rd, 2012 10:37 AM
How to draw a Venn diagram of ((a=>b)=>a)=>a? AINtKpkC3BBNn Applied Math 0 October 2nd, 2011 08:16 PM
venn diagram Jungelsucks Applied Math 1 September 10th, 2011 09:39 AM
[HELP]Venn's Diagram herohenson Advanced Statistics 2 January 26th, 2010 09:09 PM





Copyright © 2019 My Math Forum. All rights reserved.