Solve Circle Puzzle: 18 Math, 19 History, 16 Art

[Jadaav]

I know, that probably this will sound to be a dumb question but I can't find the solution to it. So if anyone could help please ?

Homework Statement

In a class of 40 pupils,

18 take Mathematics
19 take History
16 take Art
6 take both Mathematics and History
5 take both History and Art
7 take Maths and Art
and 3 take any of the 3 subjects

(a) Draw a venn diagram to show the given information

(b) Use the diagram to find the number of pupils who take all the 3 subjects

The Attempt at a Solution

The part " 3 take any of the 3 subjects " confuses me.

Edit : If possible post the link to the image of the Venn Diagram with the works.

 

[Jadaav]

I tried doing it by drawing a Venn diagram with 3 sets intersecting each other. I placed X where all the 3 sets intersect. And then I came to a point where I was stuck at -2X+35=40.

How can the answer be negative ? So that's where I am.

 

[ehild]

and 3 take any of the 3 subjectsThe part " 3 take any of the 3 subjects " confuses me.

I think that was meant "3 do not take any of the 3 subject".

Show your Venn Diagram. ehild

 

[ArcanaNoir]

I had a problem very similar to this one (are you using the new book by Tsokos?) and I solved it using a venn diagram as a little guide but doing all the real work with a system of equations that I set up like a matrix and row-reduced.

I did it by letting each variable equal one non-intersecting part of the diagram.

For example, if I had 12 cupcakes, 6 had sprinkles, and 10 had frosting. How many had sprinkles and frosting? I would let sprinkles and frosting = b, sprinkles only equal s, and frosting only equal f. Then, 12=b+s+f, b+s=6 and b+f=10. Then you have enough equations to find each variable.

 

[Jadaav]

I think that was meant "3 do not take any of the 3 subject".

Show your Venn Diagram.


ehild

The question can't be wrong because I got this question in a small exam.

 

[ArcanaNoir]

Have you made any progress on it?

 

[ehild]

The question can't be wrong because I got this question in a small exam.

The question can be wrong. Or you copied it wrong. Ask your teacher, what the sentence "3 take any of the 3 subjects" mean.

In problems like that, there must be a sentence indicating the number of those who do not belong to any of the sets. It can be that everybody takes at least one of those 3 objects, or there are 3 people who do not take any of them. Try to solve both cases.
If you add all people who study either Maths or History or Arts, you count those twice who study two objects and those who study all tree ones, you count tree times.

Find how many people belongs to each coloured fields and write in.

x students study all three objects. 6 people study both Maths and History, but the number 6 includes those who study all tree, so 6-x study only Maths and History. Find how many study History and Arts but no Maths, and how many study Arts and Maths, but no History.
Then find the number of people who study only one object: Maths or Arts or History, exclusively. If you add the numbers belonging to each different field and add those who do not take any object you get the number of the student in the class.

Add

 

[Jadaav]

Have you made any progress on it?

Still stuck there. When my friends and me got this question for the assessment, we asked the teacher, if the question was wrong. He said no, and that its good. He said, used your mind, you'll find it.

 

[ehild]

Why did you not ask the meaning of that sentence?

I can not help more. Yo do not have enough information, but have a meaningless sentence. ehild

 

[Jadaav]

Why did you not ask the meaning of that sentence?

I can not help more. Yo do not have enough information, but have a meaningless sentence.


ehild

I did, but he told me he couldn't give any tips on it, and that if he did, the solution would be too easy and everyone would get 100.

The bad thing is that, he's not at my school anymore. So can't ask him now:(

 

[HallsofIvy]

I'm inclined to think it was "3 take all of the 3 subjects" rather than "3 take any of the 3 subjects".