In a certain school, the pupils have to study Maths, Science, or Geography. Each pupil must at least study one subject. Among a group of 40 pupils, 20 are studying Maths, 22 are studying Science, and 28 are studying Geography. 12 are studing both Maths and Science, 14 are studying both Science and Geography, and 15 are studying both Maths and Geography. How many pupils are studing all 3 subjects?
The answer is 11 but I need the workings CLEARLY please. Best to include explanations beside each step as well. Please try to respond in 150 mins time from the time of this posting.
2006-09-14 01:30:58 · 5 answers · asked by miss flames 1 in Education & Reference ➔ Homework Help
Wow, this is tough. You are going to have SEVEN equations in SEVEN unknowns. The seven unknowns are the numbers who do Math-only, Science-only, Geog-only, Math+Science, Math+Geog, Science+Geog, and Everything. The equations come from the given data. Check each one of these against each datum, to see what it means.
(1) 40 = MO + SO + GO + MS + MG + SG + EV
(2) 20 = MO + MS + MG + EV
(3) 22 = SO + MS + SG + EV
(4) 28 = GO + MG + SG + EV
(5) 12 = MS + EV
(6) 14 = SG + EV
(7) 15 = MG + EV
There are hundreds of ways to subtract these equations from each other to form equations with less and less variables until you end up with the one you want, 11 = EV. One of the cleanest is this.
(2) - (5) gives 8 = MO + MG
(3) - (6) gives 8 = SO + MS
(4) - (7) gives 13 = GO + SG
Add all these together to get 29 = MO + SO + GO + MG + MS + SG, then subtract that from equation (1). Bingo! 11 = EV.
2006-09-14 02:00:11 · answer #1 · answered by Anonymous · 2⤊ 0⤋
nAUBUC will be the no of students in the class
A=set of Maths
B=set of science
C=set of geography
studying math and science AintB
science and Geography BintC
studying math and Geo AintC
studying all the three A int B int C
n of AUBUC=n(A)+n(B)+n(C)-nAintB-nBintC-nAintC+nAintBintC
int read as intersection
40=20+22+28-12-14-15+x
x=40+41-70=11
so 11 study all the tree subjects
2006-09-14 01:42:22 · answer #2 · answered by raj 7 · 3⤊ 0⤋
Use a Venn diagram, i.e. a box with circles in it each circle representing a subject. Make it so that the circles overlap and four composite regions appear in the middle.
Then add the data and see how it should add up to the total.
That should clear things up instead of working solely with set notation- like it or not most humans fancy pictures over words!
2006-09-14 01:52:07 · answer #3 · answered by yasiru89 6 · 0⤊ 0⤋
LOL
You need to do your own homework assignments honey. That's why they call it LEARNING.
2006-09-14 01:32:57 · answer #4 · answered by kja63 7 · 0⤊ 0⤋
Time to grow up and do your own homework !!!
2006-09-14 01:34:36 · answer #5 · answered by philski333 5 · 0⤊ 0⤋