MHB Draw a venn diagram and include the given information

[mathlearn]

Problem

It was revealed that out of 40 persons who visited a medical clinic , 20 heart diseases and 25 had diabetes. All those who had heart diseases and all those had diabetes suffered from stress too. 3 persons suffered from stress only had 4 persons did not suffer from stress.

i.Draw a Venn Diagram to depict this information and write down in it , the number of elements belonging to each region.

ii.How many persons had diabetes but did not have heart diseases

Workings

Okay So this is how a picture the Venn diagram should be.

View attachment 6057

Many Thanks (Happy)

 

[MarkFL]

We aren't given how many suffer both from heart disease AND diabetes, so we'll call that number $x$ and then fill in what we do know:

View attachment 6058

Now, we know the sum of all the areas is 40, so we may write:

$$(20-x)+x+(25-x)+3+4=40$$

Now, we just need to solve for $x$...(Thinking)

 

[mathlearn]

We aren't given how many suffer both from heart disease AND diabetes, so we'll call that number $x$ and then fill in what we do know:

Now, we know the sum of all the areas is 40, so we may write:

$$(20-x)+x+(25-x)+3+4=40$$

Now, we just need to solve for $x$...(Thinking)

Thank you very much (Happy)(Party)

$$(20-x)+x+(25-x)+7=40$$
$$(20)+(25-x)+7=40$$
$$(52-x)+7=40$$
$$-x=40-52$$
$$x=12$$

Now I updated the Diagram,

https://www.physicsforums.com/attachments/6059._xfImport

Many Thanks :)

Update :I have started a new thread for the second part of this question :http://mathhelpboards.com/pre-algebra-algebra-2/part-2-draw-venn-diagram-include-given-information-19726.html#post90091

 

[MarkFL]

Good job! (Star)

In the future, it's okay to post a follow-up question in the same thread (a question that pertains to the original question), we just don't want completely new questions tagged onto an existing thread. :D

 

[HallsofIvy]

Thank you very much (Happy)(Party)

$$(20-x)+x+(25-x)+7=40$$
$$(20)+(25-x)+7=40$$
$$(52-x)+7=40$$

The "+ 7" here is wrong. That 7 is already included in the "52".

$$-x=40-52$$

That error was corrected here.

$$x=12$$

Now I updated the Diagram,
Many Thanks :)

Update :I have started a new thread for the second part of this question :http://mathhelpboards.com/pre-algebra-algebra-2/part-2-draw-venn-diagram-include-given-information-19726.html#post90091

 

[mathlearn]

The "+ 7" here is wrong. That 7 is already included in the "52". That error was corrected here.

(Happy) (Smile) (Party) Thanks for the catch