URGENT MATHS Q. FOR TEST TOMORROW

Uranos · Post by **Uranos** » 24 May 2006 05:29

70 people speak english, 50 speak french, 50 speak japanese. 15 speak french and japanese, 25 speak english and french, and 30 speak japanese and english

how many speak all 3?

Iron Clad Ben · Post by **Iron Clad Ben** » 24 May 2006 09:23

I think the problem is short one known variable. How many people are there in total? I could be wrong, but I think that needs to be a known.

My answer is 15 people speak all 3, but I'm not 100% sure. Tough problem, still haven't figure out way to structure it well mathematically.

SlashC · Post by **SlashC** » 24 May 2006 13:15

Question:
70 people speak english, 50 speak french, 50 speak japanese. 15 speak french and japanese, 25 speak english and french, 30 speak japanese and english, and there are 105 people in total

how many speak all 3 languages?

Solution:

1) draw a 3 circle venn diagram and logically determine what each piece of information given in the question represents in the venn diagram

Some examples:

2) Determine the areas of the venn diagram that are unknown and define them as variables:

Let A = number of people that speak all 3 languages
Let Fr = number of people that only speak french
Let En = number of people that only speak english
Let Ja = number of people that only speak japanese

3) Write out the equations. There will be 4 equations. 3 of them are adding up the areas within each circle and the fourth equation is adding up all the areas of the entire venn diagram.

The equations are:

i) 50 = (30-A) + (15-A) + Ja + A
ii) 70 = (30-A) + (25-A) + En + A
iii) 50 = (25-A) + (15-A) + Fr + A
iv) 105 = Ja + En + Fr + (30-A) + (25-A) + (15-A) + A

Plugging the 4 equations into a matrix and solving simultaneously we find that

A = 5
Ja = 10
En = 20
Fre = 15

So there are 5 people that speak all 3 languages.

Iron Clad Ben · Post by **Iron Clad Ben** » 24 May 2006 13:49

Rory, NICE!

SlashC wrote:there are 105 people in total

How did you calculate this? I don't understand how you were able to derive this number.

pips · Post by **pips** » 24 May 2006 14:23

Wow I never saw that before. Cool.

SlashC · Post by **SlashC** » 24 May 2006 14:24

Yeah, originally I had a system with 5 variables and 4 equations. I msged Alex and asked him for the total number of people (he forgot to put it in the original question).

Iron Clad Ben · Post by **Iron Clad Ben** » 24 May 2006 15:21

Ahhh OK. I don't feel so stupid now. My instincts were right, I had too many unknowns and not enough equations to solve them!

Uranos · Post by **Uranos** » 27 May 2006 18:08

Sorry guys i forgot to put it as Slash C said

Thanks for the help. I understand it now