SOLUTION: Each student in an international study group speaks English, Japanese, or Spanish. Of these students, 100 speak English, 50 speak Japanese, 100 speak Spanish, 45 speak English and

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Question 143089This question is from textbook Integrated Algebra 1
: Each student in an international study group speaks English, Japanese, or Spanish. Of these students, 100 speak English, 50 speak Japanese, 100 speak Spanish, 45 speak English and Spanish, 10 speak English and Japanese, 13 speak Spanish and Japanese, and 5 speak all three languages. How many students do not speak English?
The answer I got is 163 students. Is it correct? This question is from textbook Integrated Algebra 1

Found 2 solutions by zephyr, richwmiller:
Answer by zephyr(9) About Me  (Show Source):
You can put this solution on YOUR website!
Sorry, but no >.<

I think I know where you got wrong, but to explain the full question, draw a venn diagram.

Like you said,

100 people speak english,

100 people speak spanish

and 50 people speak japanese

But if i'm right, the 100 people who speak english also includes the people who speak english and spanish, and the people who speak english and japanese. Do you get it now?

Draw a venn diagram, like this
http://hbswk.hbs.edu/images/chart_2469_figure1.gif
(If i'm not allowed to put down links, I'm sorry >.<)
Label them, (I'm sure you've done charts like this before) but hold on a second before you fill it out.

Let's start from the middle

5 speak all 3 languages. So put that down, in fact, put down the english and japanese people,the japanese and spanish people, and the spanish and english people. Then STOP!

Done? Okay, let's start from the "only english" section now. there should be 10 in the english and japanese, 5 in the trilingual section, and 45 in the english and spanish section.
Add those up
10%2B5%2B45=60
so that's the number of people who speak english and at least one other language, but because we're trying to find out what amount of people ONLY speaks english, you subtract that from the number of people who at least speak english (100). So it looks like this.
100-60=40
Therefore, 40 people only know english.
Now do that with the spanish only, and japanese only.

(Spanish answer: 45%2B5%2B13=63, 100-63=37 So 37 people only speak Spanish)

(Japanese answer: 10%2B5%2B13=28, 50-28=22 So only 22 people speak Japanese)

Now we add the amount of people who only speak spanish, and only speak japanese together. (22%2B37=59) But aren't we forgetting something? The people who speak Japanese AND Spanish of course ^^ So we add that too. (59%2B13=72) Therefore, only 72 people don't speak English.
(Hope it helped! If I wasn't too confusing -_-' Good Luck!)

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!

There are 187 people and 100 of them Speak English so 87 do not speak English.
5 speak all three three
so 5 only speak eng and Jap 10-5=5
so 8 only speak Jap and spanish 13-5=8
so 40 only speak eng and spanish 45-5=40
english only 100-40-5-5=50
Jap DISABLED_event_only= 50-5-5-8=32
span only 100-5-8-40=47
non eng = 47+32+8=87 don't speak Eng
see venn diagram