SOLUTION: If there are five people in a room. 3 of them are studying math. 4 people are studying science. How many people are studying both math and science, if one person is studying neit

Algebra.Com
Question 1140169: If there are five people in a room. 3 of them are studying math. 4 people are studying
science. How many people are studying both math and science, if one person is
studying neither math nor science?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
This is a Venn diagram with 2 intersecting
circles. There is 1 person outside of both circles
( math and science circles ), so
are in the circles. Label as follows:
X = only studies math
Y = studies both
Z = only studies science
(1) X + Y + Z = 4
(2) X + Y = 3 ( given )
(3) Y + Z = 4 ( given )
-------------------------
From (1) and (3), X must be zero
So, from(2), Y = 3 , and plug this into (3)
Z = 1
------------------------
So, 3 people are studying both.
Get another opinion if needed
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.

From these 5 people, separate the one who studying neither Math nor Science.


You will get then 4 persons, each of which is studying some of the two subjects.


But you are given that four of the persons are studying Math - hence, these 4 are studying Math. 


Further, that three, who studying Science, are among that four.  Hence, 3 persons are studying both subjects.


ANSWER.  3 persons are studying both subjects.


RELATED QUESTIONS

there are 20 people in a room. 8 of them are wearing socks and 13 of them are wearing... (answered by stanbon)
In a group of 30 students, 12 are studying mathematics, 18 are studying English, 8 are... (answered by richwmiller)
Two thirds of the people in a room are seated in three fourths of the chairs. The rest of (answered by richwmiller)
Eighteen people in the room were wearing glasses.If 45% of the people wear glasses,how... (answered by ewatrrr)
There are a number of people in a roo and each person shakes hands once with each of the... (answered by MathLover1)
1) There are 10 people in the room. 6 are male and 4 are female. 5 of them have been... (answered by stanbon)
There are 60 tables in a restaurant, with 25% of them seating 2 people. The tables... (answered by stanbon)
There are 60 tables in a restaurant, with 25% of them seating 2 people. The tables... (answered by jim_thompson5910,stanbon)
In a fast-food restaurant, the ratio of people eating hamburgers to people eating chicken (answered by Fombitz)