need help on venn diagrams please :)

dlofnep

I'll present the question and what I have so far so you have an understanding of what I'm stuck on... Thanks in advance for the help. My exam is tomorrow, so sooner I get help this, the better

Question:


In a PC store, 300 people bought software packages over a one-week period. Among the software packages sold were AutoCAD (A), Microsoft Office (M) and Adobe Photoshop (P).

84 people bought AutoCAD, 186 people bought Microsoft Office and 108 people bought Adobe Photoshop. 54 people bought AutoCAD and Microsoft Office, 42 bought AutoCAD and Adobe Photoshop and 24 bought all 3 software packages. 48 people bought other software packages which have not being mentioned.

Using a Venn diagram, find out how many people bought both Microsoft Office and Adobe Photoshop only.

What I have so far:

Obviously, we have the intersection of all 3, being 24. Start at the middle and work our way out. Fill in the intersections provided and subtract the total of A's intersections from A's total to give the A only. No problem. I have that down, so my Venn Diagram is looking like this so far.



Now I'm stuck to fill out the rest of the values. Could anyone suggest from here how I can find how many people bought both Microsoft Office and Adobe Photoshop only? when I'm provided with all 3 intersections in a venn diagram, it's no problem - but there is a chance I will have to answer this type of venn diagram so I want to be prepared.

If anyone can help, I'll buy you a pint if you're ever in Waterford!

Thanks in advance guys! *crosses fingers*

John.

dlofnep

I think I have it right so far?

Anyone?

Mushy

Ok, only so far now, yes you do have it right. What Im about to give you is...unfortunately not the answer...but just further figures that I've calculated.

132 more people to go into Microsoft Offfice
66 more for Adobe
168 more for the total thing, which will decrease obviously to nothing as you already have 48 in the universal set box.

I'll get back to it now again in a minute

dlofnep

ok thanks mushy

reg_anam

haven't done maths for many years but this may help - maybe ?

M incl interstection 132
P incl intersection 66
total 192

add all A 84 282

add the ouside 48 330

but total max is 300 => intesection P and M is 30 (330 - 300)

sure there is a nicer way to present it

let me know if I'm right !

Mushy

What I did was take the 132 left over for Office, take it away from total left over(168), then take that 26 from Adobe, which left me with 30 as the intersection figure. Thats one way.

Another way was to take the Adobe figure(66) from the total left over, and thats the Office figure on its own(102). Take away the Office remainder figure(132) from left over figure, which leaves 36, and that is the Adobe figure for its own. Then that leaves 30 to be the intersection of Office and Adobe.

Now all that seems to easy(if can be understood from the way i said it), so Im doubting if its right. But it comes up with 30 again

dlofnep

thank you, both of you!

Ah, it all comes down to algebra.

Call those who took microsoft office solely A, those who took both MS Office and Photoshop B (the intersection people), and those who took Photoshop solely C.

You have U, everything in the Venn diagram should be equal to that. So that's...

300 = A + B + C + 12 + 30 + 18 + 24 + 48;

A + B + C = 168 [Equation (1)]

Then you're also told that 186 people bought MS Office. So that'd be...

186 = 30 + 24 + B + C;

B + C = 132 [Equation (2)]

And you're also told that 108 people bought Photoshop, so that'd be...

108 = 18 + 24 + A + B;

A + B = 66 [Equation (3)]

Sub (2) and (3) into (1) and everything will pop out.

dlofnep

thank you