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At Steptoe college, all 200 students must know at least one foreign language dutch, polish, or turkish. Equal number of students know each of the languages a class surves shows that: 50 students know polish and dutch, 20 students know dutch and turkish and 40 students know polish and turkish. How many students know polish but not dutch or turkish? Only 13 students know all 3 languages.

Goldsteine said:

At Steptoe college, all 200 students must know at least one foreign language dutch, polish, or turkish. Equal number of students know each of the languages a class surves shows that: 50 students know polish and dutch, 20 students know dutch and turkish and 40 students know polish and turkish. How many students know polish but not dutch or turkish? Only 13 students know all 3 languages.

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Hint: Use Venn diagram.

Please read the post titled "Read before Posting".

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

Steptoe College question

I am redoing this problem from a math hw question. I can't seem to get the right answers and my professor said I need to do it on my own. I have the venn diagram written out, but the numbers don't seem to add up. Please help! thank you!

baller26 said:

I am redoing this problem from a math hw question.

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You're talking about Goldsteine's exercise, yes?

If so, please describe your Venn diagram, your numbers, and your arithmetic.

Otherwise, you need to start your own thread and post the exercise.

Cheers :cool:

goldstein

yes i am asking about this question...

At Steptoe college, all 200 students must know at least one foreign language dutch, polish, or turkish. Equal number of students know each of the languages a class surves shows that: 50 students know polish and dutch, 20 students know dutch and turkish and 40 students know polish and turkish. How many students know polish but not dutch or turkish? Only 13 students know all 3 languages.

my venn diagram consists of having...

polish dutch

37
27 13 7
turkish

37- is the number that is between polish and dutch
13- is the middle number because 13 know all 3
27- is between polish and turkish
7- is between dutch and turkish

I am stuck from here. I keep getting numbers that don't make sense.

This is what I came up with but idk if its right

ALWAYS start a word problem by writing down a brief description of each relevant unknown and matching it with a unique letter.

But what is relevant? You chose to use a Venn diagram to figure it out. GREAT idea. Draw three intersecting circles.

The Venn diagram defines how many non-overlapping areas?

Seven. Label them.

\(\displaystyle a = \#\ of\ students\ who\ know\ all\ three\ languages.\)

\(\displaystyle b = \#\ of\ students\ who\ just\ know\ Dutch\ and\ Polish.\)

\(\displaystyle c = \#\ of\ students\ who\ just\ know\ Dutch\ and\ Turkish.\)

\(\displaystyle d = \#\ of\ students\ who\ just\ know\ Polish\ and\ Turkish.\)

\(\displaystyle e = \#\ of\ students\ who\ just\ know\ Dutch.\)

\(\displaystyle f = \#\ of\ students\ who\ just\ know\ Polish.\)

\(\displaystyle g = \#\ of\ students\ who\ just\ know\ Turkish.\)

SECOND STEP, write down the information given in words in the problem in mathematical form using your assigned letters.

\(\displaystyle a + b + c + d + e + f + g = 200.\)

Adding up all seven non-overlapping areas gets total with no possibility of double counting.

Now you try to put all the other information in the problem into mathematical form, using these symbols and your Venn diagram as a guide. Show us what you get. If you get stuck, show us how far you got and ask specific questions.

baller26 said:

I am stuck from here. I keep getting numbers that don't make sense.

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We are unable to see what you're actually doing to arrive at numbers that don't make sense, so how can we determine what you've done incorrectly?

Your Venn diagram looks good, to me.

Now it's time to write some equations.

As Jeff suggested, we define symbols for unknowns first. (Otherwise, how could we write down unknown numbers?)

d = number of students who only know Dutch

p = number of students who only know Polish

t = number of students who only know Turkish

How many students know Polish? Look at your circle P and add them up:

p + 27 + 13 + 37

We see that p + 77 students know Polish.

Follow the same reasoning, to express the number of students who know Dutch.

An equal number of students know Polish and Dutch, so we may write:

p + 77 = d + 57

Keep going; use symbol t as well.

There is also an equation that you may write that involves the number 200. Can you figure out that equation?

You now have a system of equations involving three symbols. Solve for symbol p because that's what the exercise asks for.

Let us know, if you get stuck again.

Cheers :cool: